theoretical physics research papers

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Theoretical physics articles within Nature

Article 15 May 2024 | Open Access

Wavefunction matching for solving quantum many-body problems

An approach called wavefunction matching transforms particle interactions so that their wavefunctions match those of easily computable interactions, to allow for calculations of quantum many-body systems that would otherwise be difficult or impossible.

• Serdar Elhatisari
• , Lukas Bovermann
•  &  Gianluca Stellin

Article 27 March 2024 | Open Access

High-threshold and low-overhead fault-tolerant quantum memory

An end-to-end quantum error correction protocol that implements fault-tolerant memory on the basis of a family of low-density parity-check codes shows the possibility of low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.

• Sergey Bravyi
• , Andrew W. Cross
•  &  Theodore J. Yoder

Nature Careers Podcast | 17 November 2023

Scientific illustration: striking the balance between creativity and accuracy

A misleading image in a medical textbook could have life and death implications, but some disciplines can deploy myth and metaphor to convey their science through art.

• Julie Gould

Article 04 October 2023 | Open Access

Universality in long-distance geometry and quantum complexity

Many different homogeneous metrics on Lie groups, which may have markedly different short-distance properties, are shown to exhibit nearly identical distance functions at long distances, suggesting a large universality class of definitions of quantum complexity.

• Adam R. Brown
• , Michael H. Freedman
•  &  Leonard Susskind

Article | 12 April 2023

Build-up and dephasing of Floquet–Bloch bands on subcycle timescales

The build-up and dephasing of Floquet-–Bloch bands is visualized in both subcycle band-structure videography and quantum theory, revealing the interplay of strong-field intraband and interband excitations in a non-equilibrium Floquet picture.

• , M. Schüler
•  &  R. Huber

Obituary | 24 January 2023

Alexander Müller (1927–2023)

Physicist and co-discoverer of high-temperature superconductivity.

• Joseph D. Martin

News | 20 December 2022

Hint of crack in standard model vanishes in LHC data

Discrepancy in measurement of a type of particle decay had raised hopes of new physics.

• Davide Castelvecchi

News & Views | 21 November 2022

Obstacles need not impede cooperation in active matter

A theory shows that active agents can cooperate in the presence of disorder — a result that could inform the design of robots that organize on rough surfaces, or show how cells migrate en masse.

• Sam Cameron
•  &  Tannie Liverpool

Article | 12 October 2022

Attosecond clocking of correlations between Bloch electrons

By forcing electron–hole pairs onto closed trajectories attosecond clocking of delocalized Bloch electrons is achieved, enabling greater understanding of unexpected phase transitions and quantum-dynamic phenomena.

• J. Freudenstein
• , M. Borsch

Article | 20 July 2022

Dynamical topological phase realized in a trapped-ion quantum simulator

A dynamical topological phase with edge qubits that are dynamically protected from control errors, cross-talk and stray fields, is demonstrated in a quasiperiodically driven array of ten 171 Yb + hyperfine qubits in a model trapped-ion quantum processor.

• Philipp T. Dumitrescu
• , Justin G. Bohnet
•  &  Andrew C. Potter

Research Briefing | 13 July 2022

The knotty problem of tuning an instrument

Tuning the resonances of an object is crucial in many settings, from musical instruments to ultrasensitive detectors for electromagnetic and gravitational waves. This task might seem straightforward but its mathematical description has been shown to involve rich topological structures known as knots and braids.

News | 30 June 2022

Physicists spellbound by deepening mystery of muon particle’s magnetism

Theoretical predictions move closer to experimental results, but questions remain about possible gaps in the standard model of particle physics.

Article 22 June 2022 | Open Access

Many-body theory of positron binding to polyatomic molecules

A many-body theory of binding interactions between positrons and polar and nonpolar molecules is developed, showing agreement with experimental data up to within 1%.

• Jaroslav Hofierka
• , Brian Cunningham
•  &  Dermot G. Green

News | 07 April 2022

Particle’s surprise mass threatens to upend the standard model

Data from an old experiment find that the mass of the W boson is higher than theory predicts, hinting at future breakthroughs.

•  &  Elizabeth Gibney

Where I Work | 25 October 2021

Surmounting challenges with a passion for science

Insight is more important than vision in theoretical physics, says Sofia Qvarfort.

• Chris Woolston

News | 16 July 2021

The vanishing neutrinos that could upend fundamental physics

The search for exotic ‘Majorana’ particles that could solve a big antimatter mystery is ramping up around the world.

News & Views | 26 May 2021

Trip frequency is key ingredient in new law of human travel

An analysis of mobile-phone tracking data has revealed a universal pattern that describes the interplay between the distances travelled by humans on trips and the frequency with which those trips are made.

• Laura Alessandretti
•  &  Sune Lehmann

News & Views | 05 May 2021

Prediction for magnetic moment of the muon informs a test of the standard model of particle physics

A new first-principles computation of the effect that creates most uncertainty in calculations of the magnetic moment of the muon particle has been reported. The results might resolve a long-standing puzzle, but pose another conundrum.

• Harvey B. Meyer

News & Views | 14 April 2021

An exceptional view of phase transitions in non-equilibrium systems

Phase transitions in certain non-equilibrium systems cannot be described using the classical laws of statistical mechanics. A mathematical approach involving features called exceptional points now solves this far-reaching problem.

• Cynthia J. O. Reichhardt
•  &  Charles Reichhardt

News & Views | 04 November 2020

Competition at nuclear extremes explains why neutrons drip off nuclei

The neutron drip line refers to the maximum number of neutrons that can be packed into the atomic nuclei of each chemical element. A mechanism has been proposed that could explain the long-debated origin of this drip line.

• Calvin W. Johnson

Article | 07 October 2019

Axionic charge-density wave in the Weyl semimetal (TaSe 4 ) 2 I

In the charge-density-wave Weyl semimetal (TaSe 4 ) 2 I, an axion is observed and identified as a sliding mode in the charge-density-wave phase characterized by anomalous magnetoelectric transport effects.

• , B. Bradlyn
•  &  C. Felser

Books & Arts | 03 September 2019

Deciphering dark matter: the remarkable life of Fritz Zwicky

Jaco de Swart enjoys a biography of the scientist who pioneered findings on dark matter and supernovae.

• Jaco de Swart

News | 06 August 2019

Speculative ‘supergravity’ theory wins US$3-million prize

Three physicists honoured for theory that has been hugely influential — but might not be a good description of reality.

• Zeeya Merali

Obituary | 17 June 2019

Murray Gell-Mann (1929–2019)

Theoretical physicist who won a Nobel for codifying fundamental particles.

• Robert P. Crease

Books & Arts | 16 April 2019

A struggle for the soul of theoretical physics

A riposte to the view that mathematics has led physics astray beguiles Jon Butterworth.

• Jon Butterworth

News | 30 January 2019

Black-hole jets begin to reveal their antimatter secrets

The first simulations of matter and antimatter particles swirling around a rotating black hole hint at the origins of the enigmatic jets.

News & Views | 29 August 2018

Gravity measured with record precision

The gravitational constant, G , which governs the strength of gravitational interactions, is hard to measure accurately. Two independent determinations of G have been made that have the smallest uncertainties so far.

• Stephan Schlamminger

News & Views | 13 August 2018

Special relativity validated by neutrinos

Neutrinos are tiny, ghost-like particles that habitually change identity. A measurement of the rate of change in high-energy neutrinos racing through Earth provides a record-breaking test of Einstein’s special theory of relativity.

• Matthew Mewes

Books & Arts | 12 June 2018

How the belief in beauty has triggered a crisis in physics

Anil Ananthaswamy parses Sabine Hossenfelder’s analysis of why the field is at an impasse.

• Anil Ananthaswamy

Books & Arts | 08 May 2018

Richard Feynman at 100

Paul Halpern celebrates the oeuvre of the brilliant, unconventional scientist.

• Paul Halpern

Editorial | 20 March 2018

Fourier’s transformational thinking

The mathematics of Joseph Fourier, born 250 years ago this week, shows the value of intellectual boldness.

Books & Arts | 05 December 2017

The doubly dextrous physics of Enrico Fermi

Catherine Westfall lauds a candid life of a Manhattan Project scientist at home in theory and experimentation.

• Catherine Westfall

News | 09 November 2017

Dark-matter hunt fails to find the elusive particles

Physicists begin to embrace alternative explanations for the missing material.

• Elizabeth Gibney

News & Views | 02 November 2017

Quarks fuse to release energy

In nuclear fusion, energy is produced by the rearrangement of protons and neutrons. The discovery of an analogue of this process involving particles called quarks has implications for both nuclear and particle physics. See Letter p.89

• Gerald A. Miller

News | 09 October 2017

LIGO's unsung heroes

Nature highlights just a few of the people who played a crucial part in the discovery of gravitational waves — but didn’t win the Nobel Prize.

Books & Arts | 05 October 2017

Theoretical physics: When the doer met the dreamer

Graham Farmelo applauds a study on the productive friendship of two very different physicists.

• Graham Farmelo

Letter | 20 July 2017

Experimental signatures of the mixed axial–gravitational anomaly in the Weyl semimetal NbP

A positive magneto-thermoelectric conductance is observed in the Weyl semimetal niobium phosphide, suggesting the presence of the elusive mixed axial–gravitational anomaly.

• Johannes Gooth
• , Anna C. Niemann
•  &  Kornelius Nielsch

News | 13 July 2017

Tricks to mute quantum noise aid hunt for gravitational waves

Physicists find ways to make LIGO and other gravitational-wave detectors even more sensitive.

News | 01 June 2017

Neutron stars set to open their heavy hearts

Space mission will peer inside the densest matter in the Universe.

News | 19 April 2017

Physicists excited by latest LHC anomaly

A series of odd findings have theorists hoping for new particles.

News | 13 April 2017

Muons’ big moment could fuel new physics

Fermilab experiment to measure muon magnetic moment more precisely might reveal unknown virtual particles.

News | 30 March 2017

Battle between quantum and thermodynamic laws heats up

Physicists try to rebuild the laws of heat and energy for processes at a quantum scale.

News & Views | 02 November 2016

Axions exposed

Physicists are hunting for a particle called the axion that could solve two major puzzles in fundamental physics. An ambitious study calculates the expected mass of this particle, which might reshape the experimental searches. See Letter p.69 See Clarification   p.176

• Maria Paola Lombardo

News | 02 November 2016

Axion alert! Exotic-particle detector may miss out on dark matter

Supercomputer calculation suggests hypothesized particle may be heavier than thought.

Books & Arts | 12 October 2016

Physics: Fallible pontiff of physics

Graham Farmelo assesses a biography of star theorist-experimentalist Enrico Fermi.

Autumn Books | 05 October 2016

Theoretical physics: The emperor's new physics

Richard Dawid examines a critique of quantum mechanics, string theory and inflationary cosmology.

• Richard Dawid

Outlook | 28 September 2016

Dark matter: What's the matter?

The leading theory of dark matter is running out of room to hide.

Research Highlights | 24 August 2016

Neutrino search closes in

News | 19 August 2016

China, Japan, CERN: Who will host the next LHC?

Labs are vying to build ever-bigger colliders against a backdrop of uncertainty about how particle physicists will make the next big discoveries.

News | 12 August 2016

Morphing neutrinos provide clue to antimatter mystery

Excitement rises over chance of new physics from particle-du-jour.

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Journal of Physics A: Mathematical and Theoretical

Purpose-led Publishing is a coalition of three not-for-profit publishers in the field of physical sciences: AIP Publishing, the American Physical Society and IOP Publishing.

Together, as publishers that will always put purpose above profit, we have defined a set of industry standards that underpin high-quality, ethical scholarly communications.

We are proudly declaring that science is our only shareholder.

Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.

Open all abstracts , in this tab

Géza Tóth and Iagoba Apellaniz 2014 J. Phys. A: Math. Theor. 47 424006

We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramér–Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.

This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

Giuseppe Gaeta and Epifanio G Virga 2023 J. Phys. A: Math. Theor. 56 363001

In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential , a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review.

Luca Angelani 2023 J. Phys. A: Math. Theor. 56 455003

The motion of run-and-tumble particles in one-dimensional finite domains are analyzed in the presence of generic boundary conditions. These describe accumulation at walls, where particles can either be absorbed at a given rate, or tumble, with a rate that may be, in general, different from that in the bulk. This formulation allows us to treat in a unified way very different boundary conditions (fully and partially absorbing/reflecting, sticky, sticky-reactive and sticky-absorbing boundaries) which can be recovered as appropriate limits of the general case. We report the general expression of the mean exit time, valid for generic boundaries, discussing many case studies, from equal boundaries to more interesting cases of different boundary conditions at the two ends of the domain, resulting in nontrivial expressions of mean exit times.

Jing Liu et al 2020 J. Phys. A: Math. Theor. 53 023001

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér–Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.

Jacob C Bridgeman and Christopher T Chubb 2017 J. Phys. A: Math. Theor. 50 223001

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes.

These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states.

The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.

John Goold et al 2016 J. Phys. A: Math. Theor. 49 143001

This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.

Martin R Evans et al 2020 J. Phys. A: Math. Theor. 53 193001

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r , which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r . We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

Benjamin C B Symons et al 2023 J. Phys. A: Math. Theor. 56 453001

Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP -hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for noisy intermediate scale quantum devices. The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: analogue and gate-based quantum computers. While analog devices such as quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples. The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation algorithm and the quantum alternating operator ansatz framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

Sophia M Walls et al 2024 J. Phys. A: Math. Theor. 57 175301

We investigate the quantum Zeno effect (QZE) in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The QZE is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate, thus the QZE emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the QZE is stronger when the system dwells in the vicinity of certain eigenstates compared to others.

Sophie Hermann et al 2024 J. Phys. A: Math. Theor. 57 175001

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether's theorem and also give more elementary proofs based on partial phase space integration following Yvon's theorem.

Latest articles

Ananda G Maity and Samyadeb Bhattacharya 2024 J. Phys. A: Math. Theor. 57 215302

There are certain dynamics while being non-Markovian, do never exhibit information backflow. We show that if two such dynamical maps are considered in a scenario where the order of application of these two dynamical maps are not definite, the effective channel can manifest information backflow. In particular, we use quantum SWITCH to activate such a channel. In contrast, activation of those channels are not possible even if one uses many copies of such channels in series or in parallel action. We then investigate the dynamics behind the quantum SWITCH experiment and find out that after the action of quantum SWITCH both the CP (Complete Positive)- divisiblity and P (Positive)- divisibility of the channel breaks down, along with the activation of information backflow. Our study elucidate the advantage of quantum SWITCH by investigating its dynamical behaviour.

Bergfinnur Durhuus et al 2024 J. Phys. A: Math. Theor. 57 215202

We characterize the spectrum of the transition matrix for simple random walk on graphs consisting of a finite graph with a finite number of infinite Cayley trees attached. We show that there is a continuous spectrum identical to that for a Cayley tree and, in general, a non-empty pure point spectrum. We apply our results to studying continuous time quantum walk on these graphs. If the pure point spectrum is nonempty the walk is in general confined with a nonzero probability.

Humberto C F Lemos and Emmanuel Pereira 2024 J. Phys. A: Math. Theor. 57 215001

In this article, to study the heat flow behavior, we perform analytical investigations in a rotor chain type model (involving inner stochastic noises) with next and next-nearest-neighbor (NN) interactions. It is known in the literature that the chain rotor model with long range interactions presents an insulating phase for the heat conductivity. But we show, in contrast with such a behavior, that the addition of a next-NN potential increases the thermal conductivity, at least in the low temperature regime, indicating that the insulating property is a genuine long range interaction effect. We still establish, now by numerical computations, the existence of a thermal rectification in systems with graded structures.

Meng Cao et al 2024 J. Phys. A: Math. Theor. 57 215301

P L Krapivsky 2024 J. Phys. A: Math. Theor. 57 215201

A map of a set to itself admits a representation by a graph with vertices being the elements of the set and an edge between every vertex and its image. Communities defined as the maximal connected components are uni-cyclic. The distributions of the sizes of communities and lengths of cycles for unconstrained random maps is a classical subject. We call experts the images and followers the remaining vertices, and we further define prophets, egocentrics, and introverts. We introduce and analyze classes of random maps with sociological flavor.

Review articles

Piotr Mironowicz 2024 J. Phys. A: Math. Theor. 57 163002

This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations, optimize quantum states, and design efficient quantum algorithms and protocols. The paper also discusses implementational aspects, such as solvers for SDP and modeling tools, enabling the effective employment of optimization techniques in quantum information processing. The insights and methodologies presented in this paper have proven instrumental in advancing the field of quantum information, facilitating the development of novel communication protocols, self-testing methods, and a deeper understanding of quantum entanglement.

Manuel de León and Rubén Izquierdo-López 2024 J. Phys. A: Math. Theor. 57 163001

In this paper we study coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of coisotropic reduction is motivated by the fact that these dynamics can always be interpreted as Lagrangian or Legendrian submanifolds. Furthermore, Lagrangian or Legendrian submanifolds can be reduced by a coisotropic one.

J S Dehesa 2024 J. Phys. A: Math. Theor. 57 143001

M Gabriela M Gomes et al 2024 J. Phys. A: Math. Theor. 57 103001

Mathematical models are increasingly adopted for setting disease prevention and control targets. As model-informed policies are implemented, however, the inaccuracies of some forecasts become apparent, for example overprediction of infection burdens and intervention impacts. Here, we attribute these discrepancies to methodological limitations in capturing the heterogeneities of real-world systems. The mechanisms underpinning risk factors of infection and their interactions determine individual propensities to acquire disease. These factors are potentially so numerous and complex that to attain a full mechanistic description is likely unfeasible. To contribute constructively to the development of health policies, model developers either leave factors out (reductionism) or adopt a broader but coarse description (holism). In our view, predictive capacity requires holistic descriptions of heterogeneity which are currently underutilised in infectious disease epidemiology, in comparison to other population disciplines, such as non-communicable disease epidemiology, demography, ecology and evolution.

Featured articles

Tim Adamo and Sumer Jaitly 2020 J. Phys. A: Math. Theor. 53 055401

Keith Alexander et al 2020 J. Phys. A: Math. Theor. 53 045001

We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using both lattice walks and ideal chains, we find an ensemble of random, tangled open curves whose knotting is not dominated by any single knot type, a behaviour we call weakly knotted. We compare cubically confined lattice walks and spherically confined ideal chains, finding the weak knotting probability in both families is quite similar and growing with length, despite the overall knotting probability being quite different. In contrast, the probability of weak knotting in unconfined walks is small at all lengths investigated. For spherically confined ideal chains, weak knotting is strongly correlated with the degree of confinement but is almost entirely independent of length. For ideal chains confined to tubes and slits, weak knotting is correlated with an adjusted degree of confinement, again with length having negligible effect.

Yongchao Lü and Joseph A Minahan 2020 J. Phys. A: Math. Theor. 53 024001

Accepted manuscripts

Lamers et al 

The Haldane–Shastry spin chain has a myriad of remarkable properties, including Yangian symmetry and, for spin 1/2, explicit highest-weight eigenvectors featuring (the case α = 1/2 of) Jack polynomials. This stems from the spin-Calogero–Sutherland model, which reduces to Haldane–Shastry in a special 'freezing' limit.

In this work we clarify various points that, to the best of our knowledge, were missing in the literature. We have two main results. First, we show that freezing the fermionic spin-1/2 Calogero–Sutherland model naturally accounts for the precise form of the Haldane–Shastry wave functions, including the Vandermonde factor squared. Second, we use the fermionic framework to prove the claim of Bernard–Gaudin–Haldane–Pasquier that the Yangian highest-weight eigenvectors of the SU(r)-version of the Haldane–Shastry chain arise by freezing SU(r−1) spin-Calogero–Sutherland eigenvectors at α = 1/2.

Ozorio de Almeida 

The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory segments along the shell determine the phase of the Wigner oscillations in its interior. The classical transitions between any pair of energy shells, driven by a general external time dependent Hamiltonian, also have a smooth probability density. It is shown here that a further contribution to the transition between the corresponding pair of coarsegrained energy levels, which oscillates with either energy, or the driving time, is determined by four trajectory segments (two in the pair of energy shells and two generated by the driving Hamiltonian) that join exactly to form a closed compound orbit. In its turn, this sequence of segments belongs to the semiclassical expression of a compound unitary operator that 
combines four quantum evolutions: a pair generated by the static internal Hamiltonian and a pair generated by the driving Hamiltonian.
The closed compound orbits are shown to belong to continuous families, which are initially seeded at points where the classical flow generated by both Hamiltonians commute.

Christie et al 

We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, using a double-well potential model. This paper aims to bridge gaps in understanding the crossover from thermal activation to quantum tunnelling, a domain still shrouded in mystery despite extensive research. We study a Caldeira-Leggett-derived model of quantum Brownian motion and investigate the Lindblad and stochastic Schr"{o}dinger dynamics numerically, seeking to offer new insights into the transition states in the crossover region. Our study has implications for quantum computing and understanding fundamental natural processes, highlighting the significance of quantum effects on transition rates and temperature influences on tunnelling.

Additionally, we introduce a new model for quantum Brownian motion which takes Lindblad form and is formulated as a modification of the widely known model found in Breuer and Petruccione. In our approach, we remove the zero-temperature singularity resulting in a better description of low-temperature quantum Brownian motion near a potential minima.

Eliazar 

Diffusion is a generic term for random motions whose positions become more and more diffuse with time. Diffusion is of major importance in numerous areas of science and engineering, and the research of diffusion is vast and profound. This paper is the first in a stochastic `intro series' to the multidisciplinary field of diffusion. The paper sets off from a basic question: how to quantitatively measure diffusivity? Having answered the basic question, the paper carries on to a follow-up question regarding statistical behaviors of diffusion: what further knowledge can the diffusivity measure provide, and when can it do so? The answers to the follow-up question lead to an assortment of notions and topics including: persistence and anti-persistence; aging and anti-aging; spectral densities, white noise, and their generalizations; the Wiener-Khinchin theorem and its generalizations; and colored noises. Then, observing diffusion from a macro level, the paper culminates with: the universal emergence of power-law diffusivity; the three universal diffusion regimes -- one regular, and two anomalous; and the universal emergence of 1/f noise. The paper is entirely self-contained, and its prerequisites are undergraduate mathematics and statistics.

Ren et al 

In this paper, we propose two new measures: one is symmetrized skew information and the other one is standard symmetrized skew information. Firstly, we prove their properties, such as non-negativity, convexity, invariance, additivity, monotonicity and strong monotonicity. Next, we conduct research on relationships between standard symmetrized skew information and several well-known measures in one-qubit state, aiming to compare their similarities and differences. In addition, standard symmetrized skew information is used to study quantum uncertainty. We also give the definition of standard symmetrized skew information of assistance, and provide it a straightforward operational explanation for better understanding. Finally, standard symmetrized skew information can be applied to detect entanglement.

More Accepted manuscripts

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Robson Christie and Jessica Kaye Eastman 2024 J. Phys. A: Math. Theor.

Iddo Isaac Eliazar 2024 J. Phys. A: Math. Theor.

Carlos Heredia Pimienta and Josep Llosa 2024 J. Phys. A: Math. Theor.

We study the relationship between integral and infinite-derivative operators. In particular, we examine the operator $p^{\frac{1}{2}\,\partial_t^2}\,$ that appears in the theory of $p$-adic string fields, as well as the Moyal product that arises in non-commutative theories. We also try to clarify the apparent paradox raised by Moeller and Zwiebach, which highlights the discrepancy between them.

Lluís Hernández-Navarro et al 2024 J. Phys. A: Math. Theor.

Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from a cooperative behaviour. Moreover, microbes generally evolve in volatile environments that, together with demographic fluctuations (birth and death events), drastically alter population size and strain survival. Motivated by the need to better understand the evolution of AMR, we study a population of time-varying size consisting of two competing strains, one drug-resistant and one drug-sensitive, subject to demographic and environmental variability. This is modelled by a binary carrying capacity randomly switching between mild and harsh environmental conditions, and driving the fluctuating volume (total amount of nutrients and antimicrobials at fixed concentration), and thus the size of the community (number of resistant and sensitive cells). We assume that AMR is a shared public good when the concentration of resistant cells exceeds a fixed {\it concentration cooperation threshold}, above which the sensitive strain has a growth advantage, whereas resistant cells dominate below it. Using computational means, and devising an analytical treatment (built on suitable quenched and annealed averaging procedures), we fully characterise the influence of fluctuations on the eco-evolutionary dynamics of AMR, and notably obtain specific strain fixation and long-lasting coexistence probabilities as a function of the environmental variation rate and cooperation threshold. We find that microbial strains tend to coexistence, but demographic fluctuations eventually lead to the extinction of resistant or sensitive cells for small or large values of the concentration cooperation threshold, respectively. This also holds for dynamic environments, whose specific properties determine the extinction timescale.

Jeanine Shea et al 2024 J. Phys. A: Math. Theor.

Colloidal probes immersed in an active bath have been found to behave like active particles themselves. Here, we use coarse-grained simulations to investigate the mechanisms behind this behavior. We find that the active motion of the colloid cannot be simply attributed to the convective motion in the bath. Instead, the boundary of the probe contributes significantly to these adopted dynamics by causing active bath particles to spontaneously accumulate at the probe. This gathering of active bath particles then pushes the probe, thus promoting its emergent active-particle-like behavior. Furthermore, we find that the dynamic properties of the probe depend on its size in a non-monotonic way, which further highlights the non-trivial interplay between probe and bath.

Maurice de Gosson 2024 J. Phys. A: Math. Theor. 57 205303

We address the problem of the reconstruction of quantum covariance matrices using the notion of Lagrangian and symplectic polar duality introduced in previous work. We apply our constructions to Gaussian quantum states which leads to a non-trivial generalization of Pauli's reconstruction problem and we state a simple tomographic characterization of such states.

Ondřej Kubů et al 2024 J. Phys. A: Math. Theor.

This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to non-subgroup-type coordinates. We find three new systems, two with magnetic fields polynomial in Cartesian coordinates and one with unbounded exponential terms. The limit in the parameters of the integrals yields a new parabolic cylindrical system; the limit of vanishing magnetic fields leads to the free motion. This confirms the conjecture that non-subgroup type integrals can be related to separable systems only in a trivial manner.

Julio C Andrade and Christopher G Best 2024 J. Phys. A: Math. Theor. 57 205205

Andreani Petrou and Shinobu Hikami 2024 J. Phys. A: Math. Theor. 57 205204

In an attempt to generalise knot matrix models for non-torus knots, which currently remains an open problem, we derived expressions for the Harer–Zagier transform—a discrete Laplace transform—of the HOMFLY–PT polynomial for some infinite families of twisted hyperbolic knots. Among them, we found a family of pretzel knots for which, like for torus knots, the transform has a fully factorised form, while for the remaining families considered it consists of sums of factorised terms. Their zero loci show a remarkable structure, which mostly lies on the unit circle and deviates from it only in pairs.

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• 2007-present Journal of Physics A: Mathematical and Theoretical doi: 10.1088/issn.1751-8121 Online ISSN: 1751-8121 Print ISSN: 1751-8113

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• 2007-present Journal of Physics A: Mathematical and Theoretical
• 1975-2006 Journal of Physics A: Mathematical and General
• 1973-1974 Journal of Physics A: Mathematical, Nuclear and General
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• Stanford Institute for Theoretical Physics

Research in the  Stanford Institute for Theoretical Physics (SITP)  spans a wide range of topics from understanding the fundamental nature of forces, particles and space-time geometry, to condensed matter physics and quantum information.  There is considerable cross-fertilization in some of these endeavors with faculty in the  SLAC Theory Group  and the  Kavli Institute for Particle Astrophysics and Cosmology

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Quantum physics and Einstein’s theory of general relativity are the two solid pillars that underlie much of modern physics. Understanding how these two well-established theories are related remains a central open question in theoretical physics.  Over the last several decades, efforts in this direction have led to a broad range of new physical ideas and mathematical tools.  In recent years, string theory and quantum field theory have converged in the context of holography, which connects quantum gravity in certain space-times with corresponding (conformal) field theories on a lower-dimensional space-time. These developments and connections have deepened our understanding not only of quantum gravity, cosmology, and particle physics, but also of intermediate scale physics, such as condensed matter systems, the quark-gluon plasma, and disordered systems.  String theory has also led to new insights to problems in many areas of mathematics.

The interface of quantum physics and gravity is currently leading to exciting new areas of progress, and is expected to remain vibrant in the coming decade.  Researchers in the Center for Theoretical Physics (CTP) have been at the forefront of many of the developments in these directions.  CTP faculty members work on string theory foundations, the range of solutions of the theory, general relativity and quantum cosmology, problems relating quantum physics to black holes, and the application of holographic methods to strongly coupled field theories.  The group in the CTP has close connections to condensed matter physicists, astrophysicists, and mathematicians both at MIT and elsewhere.

In recent years a set of new developments has begun to draw unexpected connections between a number of problems relating aspects of gravity, black holes, quantum information, and condensed matter systems. It is becoming clear that quantum entanglement, quantum error correction, and computational complexity play a fundamental role in the emergence of spacetime geometry through holographic duality.  Moreover these tools have led to substantial progress on the famous black hole information problem, giving new avenues for searching for a resolution of the tension between the physics of black holes and quantum mechanics.  CTP faculty members Netta Engelhardt and Daniel Harlow have been at the vanguard of these developments, which also tie into the research activity of several other CTP faculty members, including Aram Harrow , whose primary research focus is on quantum information, and Hong Liu , whose research connects black holes and quantum many-body dynamics.

Holographic dualities give both a new perspective into quantum gravitational phenomena as encoded in quantum field theory, and a way to explore aspects of strongly coupled field theories using the gravitational dual. CTP faculty have played a pioneering role in several applications of holographic duality. Hong Liu and Krishna Rajagopal are at the forefront of efforts that use holography to find new insights into the physics of the quark-gluon plasma. Liu was among the first to point out possible connections between black hole physics and the strange metal phase of high temperature superconductors, and in recent years has been combining insights from effective field theories, holography, and condensed matter physics to address various issues concerning far-from-equilibrium systems including superfluid turbulence, entanglement growth, quantum chaos, thermalization, and a complete formulation of fluctuating hydrodynamics. Gravitational effective field theories play a key role in the interpretation of gravitational wave observations. Mikhail Ivanov works at the intersection of these fields with the aim of testing strong field gravity at a new precision frontier.

Even though we understand string theory better than we did in decades past, there is still no clear fundamental description of the theory that works in all situations, and the set of four-dimensional solutions, or string vacua, is still poorly understood.  The work of Washington Taylor and Barton Zwiebach combines physical understanding with modern mathematical methods to address these questions, and has led to new insights into how observed physics fits into the framework of string theory as well as the development of new mathematical results and ideas. Alan Guth ‘s foundational work on inflationary cosmology has led him to focus on basic questions about the physics of the multiverse that arises naturally in the context of the many string theory vacua, and which provides the only current natural explanation for the observed small but positive cosmological constant.

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Title: status and perspectives of neutrino physics.

Abstract: This review demonstrates the unique role of the neutrino by discussing in detail the physics of and with neutrinos. We deal with neutrino sources, neutrino oscillations, absolute masses, interactions, the possible existence of sterile neutrinos, and theoretical implications. In addition, synergies of neutrino physics with other research fields are found, and requirements to continue successful neutrino physics in the future, in terms of technological developments and adequate infrastructures, are stressed.

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Theoretical Physics

This field studies the interplay between physical theories, the insights and intuitions obtained from them, and rigorous mathematics. This applies to many parts of physics, such as classical dynamical systems, statistical mechanics, condensed matter theory, astrophysics, elementary particle theory, gravitation, and string theory. For much of the last 20 years, the work of string theorists has stimulated important developments in geometry. Seiberg-Witten theory is one prime example, which has led to work in pure mathematics.

Department Members in This Field

• Hung Cheng Theoretical Physics
• Daniel Freedman Theoretical Physics, Supergravity, Supersymmetry
• Andrei Neguț Algebraic Geometry, Representation Theory

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• Adam Kay Hydrodynamic Quantum Analogues

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• Andrey Khesin Quantum Computing
• Xinyu (Norah) Tan Quantum computing, quantum information, coding theory

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Theoretical Physics

  Karapet Mkrtchyan  and  Mantas Svazas 

Mkrtchyan, K., Svazas, M. Solutions in Nonlinear Electrodynamics and their double copy regular black holes. J. High Energ. Phys. 2022, 12 (2022).  doi.org/10.1007/JHEP09(2022)012

Théo Keseman, Hans J. Muneesamy, and Yasaman K. Yazdi.

Insights on Entanglement Entropy in 1+1 Dimensional Causal Sets, 2022 Class. Quantum Grav. 39 245004.  doi: 10.1088/1361-6382/ac5fc0

  Callum F. Duffy, Joshua Y. L. Jones, and Yasaman K. Yazdi.

Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory, 2022 Class. Quantum Grav. 39 075017  doi: 10.1088/1361-6382/ac5493

  Marko Ivin and Mathias Möbius

Their MSci project supervised by  Dr. Tim Evans  applied a novel non-perturbative approach to calculations in quantum field theory. Marko and Mathias looked at phase transitions in a simplified model of the Higgs field. It was published in Nuclear Physics B as  An Optimised Perturbation Expansion for a Global O(2) Theory  in 2000.

Edmund Hunt For his BSc project Edmund looked at a network model used to study interactions in the Minoan Aegean. He applied concepts from statistical physics to produce models of interest to archaeologists. His results formed part of a presentation at the  European Conference on Complex Systems in 2007 (ECCS 07) . This appeared in the proceedings as  Modelling Cultural Dynamics: A Macroscopic Approach To Cultural Transmission In The Prehistoric Aegean  coauthored with two physicists,  Dr. Tim Evans  and  Prof. Ray Rivers , and an archaeologist, Prof. Carl Knappett.

Tevong You As part of his MSci project, Tevong looked at a statistical physics model of  cultural transmission , that is how are ideas (memes) are exchanged in human society. In particular he asked how results are changed when the exchange is done on a variety of different types of network. His work formed part of a presentation at the European Conference on Mathematics for Industry (ECMI) in 2008. Tevong's results were used in an article for the proceedings entitled  Are Copying and Innovation Enough? , coauthored with an MSc student Doug Plato (who gave the presentation) and his project supervisor  Dr. Tim Evans .

Andrea Giometto A visiting Erasmus student, Andrea looked at the statistics of top 10 lists in models of  cultural transmission . That is if we look a list of the  y  most popular items of one type, such as music downloads or baby names, and the list is updated on a regular basis, how large are the changes to the list every week? This result can be used to fix the parameters used in models of  cultural transmission . This was written up as a paper on the  arXiv  entitled  Turnover Rate of Popularity Charts in Neutral Models , coauthored with his project supervisor  Dr. Tim Evans .

Toby Clemson In his MSci project Toby looked at a simple model of markets known as the Minority Game. His study looked at the effect on markets of introducing a more realistic social network between the brokers as this controls the flow of information between agents. His results formed the basis for a paper published in 2012 in Physica A,  The Emergence of Leadership in Social Networks .

Nicola Hopkins and Ben Kaube Nicola and Ben worked in successive years as summer students with  Dr. Tim Evans  funded by a Nuffield Undergraduate Research Bursary  and an  Imperial College UROP bursary  respectively. They looked at ways to characterise the quality of research papers which were better than a straight count of the number of citations a paper receives. This involved data on citations drawn from a research institute and from the  arXiv . Their work appeared as  Universality of Performance Indicators based on Citation and Reference Counts  which was published in Scientometrics in 2012.

Annabel Downs and Anna Hashagen , together with PhD student James Yearsley, supervised by Prof Jonathan Halliwell, co-authored a paper based on their MSci project, in which an idealized clock model was used to derive formulas for the arrival time and dwell time of the free particle. “Quantum Arrival and Dwell Times via Idealised Clocks” J.M.Yearsley ,  D.A.Downs ,  J.J.Halliwell ,  A.K.Hashagen Phys. Rev. A 84, 022109 (2011), arXiv:1106.4767 .

Rhian Hartshorn and Ariadne Whitby , together with PhD student James Yearsley, supervised by Prof Jonathan Halliwell, co-authored a paper based on their MSci project, exploring the quantum-mechanical phenomenon of backflow, in which a state of entirely positive momenta can have negative current, so that the probability flows "backwards’’. “Analytic Examples, Measurement Models and Classical Limit of Quantum Backflow” J.M.Yearsley ,  J J.Halliwell ,  R.Hartshorn ,  A.Whitby Phys. Rev. A 86, 042116 (2012), arXiv:1202.1783 .

Edward Gillman, Olivier Lennon , Meera Patel and Ivan Ramirez , supervised by Prof Jonathan Halliwell, co-authored a paper based on their MSci project, exploring the quantum-mechanical phenomenon of backflow an determining a wide class of states exhibiting it. “Quantum Backflow States from Eigenstates of the Regularized Current Operator” J.J.Halliwell ,  E.Gillman ,  O.Lennon ,  M.Patel ,  I.Ramirez J. Phys. A 46, 475303 (2013), arXiv:1309.2909 .

Jonas Evaeus , Jonathan London and Yasmin Malik , supervised by Prof Jonathan Halliwell, co-authored a paper based on their MSci project in which a new physically motivated self-adjoint time operator was derived, and also a discussion of why the conventional arrival time operator is not self-adjoint was given. "A self-adjoint arrival time operator inspired by measurement models” J.J. Halliwell ,  J. Evaeus ,  J. London ,  Y. Malik Phys. Lett. A 379, 2445 (2015), arXiv:1504.02509 .

Sophia Goldberg and Hannah Anthony From June 2012 to May 2013, Sophia and Hannah worked with Dr Tim Evans on their final year MSci project. This was looking at the way that the distribution of number of citations to papers published on one topic in the same year always seems to have the same shape, once you scale out the growth in the average number of citations over time. However most simple models fail to capture this feature. It showed that a relatively simple model, involving some copying of citations read in other papers, led to the correct behaviour. This work was published as  Modelling Citation Networks  in Scientometrics  105  (2015) 1577-1604, one of the leading journals for bibliometrics, DOI  10.1007/s11192-015-1737-9  [ arXiv:1408.2970 ]. The work was presented as a poster,  Do We Need Global and Local Knowledge of the Citation Network?  at the ISSI 2015 conference and a summary appears in the  ISSI 2015 conference proceedings .

Tamar Loach Tamar worked on a summer project with Dr Tim Evans from June to September 2013. They looked at data from  altmetric.com  which showed when an academic paper was mentioned in social media, traditional media web sites. They showed how you could use this information to rate different journals based on the attention their papers gained in such alternative (non-traditional) media. This work was presented at the ISSI 2015 conference, Ranking Journals Using Altmetrics  ( the slides for Ranking Journals Using Altmetrics  are on figshare.com) and the accompanying paper appears in the  ISSI 2015 conference proceedings  [ arXiv:1507.00451 ].

James Clough, Jamie Gollings and Tamar Loach James, Jamie and Tamar did their final year project with Dr Tim Evans from June 2011 to May 2013 as part of their MSci degree in Physics at Imperial. They looked at a particular type of network in which the vertices (nodes) are constrained by time (or an equivalent ordering). These are known as DAGs - Directed Acyclic Graphs. They did this both on theoretical models, some of which are used in the causal sets approach to quantum gravity, and on real data - a citation network derived from the arXiv preprint database. The paper is  Transitive Reduction of Citation Networks , published with open access in The Journal of Complex Networks  3  (2015) 189-203, DOI  10.1093/comnet/cnu039  [ arXiv:1310.8224 ].

Dominic Reiss and Joshua Price

Dominic and Joshua were students on the Imperial College Physics BSc course. Their final year project over the Spring term of 2013 tried to convert mathematical models used in complexity science into 3D printed objects. This was much harder than we expected for various technical reasons so it was all the more to their credit that they pushed this through to produce an actual 3D printed object based on a modified version of the forest fire model. Their project reports and code are online at figshare.com. A paper based on this work appeared as  Scuplexity: Sculpture of Complexity using 3D Printing , European Physics Letters  104  (2013) 48001, doi:  10.1209/0295-5075/104/48001  (see also  3D printing used as a tool to explain theoretical physics  and  Sculplexity: sculptures of complexity using 3D printing ).

Zhenghao Zhong

For his UROP project, Zhenghao Zhong and PhD student Santiago Cabrera, supervised by Professor Amihay Hanany, looked at various quiver gauge theories. These are 3d N=4 gauge theories whose matter content and gauge groups can be encoded in graphs called quiver diagrams. Their research focused on 3d mirror symmetry and the choice of orthogonal and special orthogonal gauge groups in the quiver diagrams and can be found here .

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See our further guidance on citing datasets.

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See our FAQ page for more information on Springer Nature's research data policy.

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This journal is committed to upholding the integrity of the scientific record. As a member of the Committee on Publication Ethics ( COPE ) the journal will follow the COPE guidelines on how to deal with potential acts of misconduct.

Authors should refrain from misrepresenting research results which could damage the trust in the journal, the professionalism of scientific authorship, and ultimately the entire scientific endeavour. Maintaining integrity of the research and its presentation is helped by following the rules of good scientific practice, which include*:

• The manuscript should not be submitted to more than one journal for simultaneous consideration.
• The submitted work should be original and should not have been published elsewhere in any form or language (partially or in full), unless the new work concerns an expansion of previous work. (Please provide transparency on the re-use of material to avoid the concerns about text-recycling (‘self-plagiarism’).
• A single study should not be split up into several parts to increase the quantity of submissions and submitted to various journals or to one journal over time (i.e. ‘salami-slicing/publishing’).
• Concurrent or secondary publication is sometimes justifiable, provided certain conditions are met. Examples include: translations or a manuscript that is intended for a different group of readers.
• Results should be presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation (including image based manipulation). Authors should adhere to discipline-specific rules for acquiring, selecting and processing data.
• No data, text, or theories by others are presented as if they were the author’s own (‘plagiarism’). Proper acknowledgements to other works must be given (this includes material that is closely copied (near verbatim), summarized and/or paraphrased), quotation marks (to indicate words taken from another source) are used for verbatim copying of material, and permissions secured for material that is copyrighted.

Important note: the journal may use software to screen for plagiarism.

• Authors should make sure they have permissions for the use of software, questionnaires/(web) surveys and scales in their studies (if appropriate).
• Research articles and non-research articles (e.g. Opinion, Review, and Commentary articles) must cite appropriate and relevant literature in support of the claims made. Excessive and inappropriate self-citation or coordinated efforts among several authors to collectively self-cite is strongly discouraged.
• Authors should avoid untrue statements about an entity (who can be an individual person or a company) or descriptions of their behavior or actions that could potentially be seen as personal attacks or allegations about that person.
• Research that may be misapplied to pose a threat to public health or national security should be clearly identified in the manuscript (e.g. dual use of research). Examples include creation of harmful consequences of biological agents or toxins, disruption of immunity of vaccines, unusual hazards in the use of chemicals, weaponization of research/technology (amongst others).
• Authors are strongly advised to ensure the author group, the Corresponding Author, and the order of authors are all correct at submission. Adding and/or deleting authors during the revision stages is generally not permitted, but in some cases may be warranted. Reasons for changes in authorship should be explained in detail. Please note that changes to authorship cannot be made after acceptance of a manuscript.

*All of the above are guidelines and authors need to make sure to respect third parties rights such as copyright and/or moral rights.

Upon request authors should be prepared to send relevant documentation or data in order to verify the validity of the results presented. This could be in the form of raw data, samples, records, etc. Sensitive information in the form of confidential or proprietary data is excluded.

If there is suspicion of misbehavior or alleged fraud the Journal and/or Publisher will carry out an investigation following COPE guidelines. If, after investigation, there are valid concerns, the author(s) concerned will be contacted under their given e-mail address and given an opportunity to address the issue. Depending on the situation, this may result in the Journal’s and/or Publisher’s implementation of the following measures, including, but not limited to:

• If the manuscript is still under consideration, it may be rejected and returned to the author.

- an erratum/correction may be placed with the article

- an expression of concern may be placed with the article

- or in severe cases retraction of the article may occur.

The reason will be given in the published erratum/correction, expression of concern or retraction note. Please note that retraction means that the article is maintained on the platform , watermarked “retracted” and the explanation for the retraction is provided in a note linked to the watermarked article.

• The author’s institution may be informed
• A notice of suspected transgression of ethical standards in the peer review system may be included as part of the author’s and article’s bibliographic record.

Fundamental errors

Authors have an obligation to correct mistakes once they discover a significant error or inaccuracy in their published article. The author(s) is/are requested to contact the journal and explain in what sense the error is impacting the article. A decision on how to correct the literature will depend on the nature of the error. This may be a correction or retraction. The retraction note should provide transparency which parts of the article are impacted by the error.

Suggesting / excluding reviewers

Authors are welcome to suggest suitable reviewers and/or request the exclusion of certain individuals when they submit their manuscripts. When suggesting reviewers, authors should make sure they are totally independent and not connected to the work in any way. It is strongly recommended to suggest a mix of reviewers from different countries and different institutions. When suggesting reviewers, the Corresponding Author must provide an institutional email address for each suggested reviewer, or, if this is not possible to include other means of verifying the identity such as a link to a personal homepage, a link to the publication record or a researcher or author ID in the submission letter. Please note that the Journal may not use the suggestions, but suggestions are appreciated and may help facilitate the peer review process.

These guidelines describe authorship principles and good authorship practices to which prospective authors should adhere to.

Authorship clarified

The Journal and Publisher assume all authors agreed with the content and that all gave explicit consent to submit and that they obtained consent from the responsible authorities at the institute/organization where the work has been carried out, before the work is submitted.

The Publisher does not prescribe the kinds of contributions that warrant authorship. It is recommended that authors adhere to the guidelines for authorship that are applicable in their specific research field. In absence of specific guidelines it is recommended to adhere to the following guidelines*:

All authors whose names appear on the submission

1) made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data; or the creation of new software used in the work;

2) drafted the work or revised it critically for important intellectual content;

3) approved the version to be published; and

4) agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

* Based on/adapted from:

ICMJE, Defining the Role of Authors and Contributors,

Transparency in authors’ contributions and responsibilities to promote integrity in scientific publication, McNutt at all, PNAS February 27, 2018

Disclosures and declarations

All authors are requested to include information regarding sources of funding, financial or non-financial interests, study-specific approval by the appropriate ethics committee for research involving humans and/or animals, informed consent if the research involved human participants, and a statement on welfare of animals if the research involved animals (as appropriate).

The decision whether such information should be included is not only dependent on the scope of the journal, but also the scope of the article. Work submitted for publication may have implications for public health or general welfare and in those cases it is the responsibility of all authors to include the appropriate disclosures and declarations.

Data transparency

All authors are requested to make sure that all data and materials as well as software application or custom code support their published claims and comply with field standards. Please note that journals may have individual policies on (sharing) research data in concordance with disciplinary norms and expectations.

Role of the Corresponding Author

One author is assigned as Corresponding Author and acts on behalf of all co-authors and ensures that questions related to the accuracy or integrity of any part of the work are appropriately addressed.

The Corresponding Author is responsible for the following requirements:

• ensuring that all listed authors have approved the manuscript before submission, including the names and order of authors;
• managing all communication between the Journal and all co-authors, before and after publication;*
• providing transparency on re-use of material and mention any unpublished material (for example manuscripts in press) included in the manuscript in a cover letter to the Editor;
• making sure disclosures, declarations and transparency on data statements from all authors are included in the manuscript as appropriate (see above).

* The requirement of managing all communication between the journal and all co-authors during submission and proofing may be delegated to a Contact or Submitting Author. In this case please make sure the Corresponding Author is clearly indicated in the manuscript.

Author contributions

In absence of specific instructions and in research fields where it is possible to describe discrete efforts, the Publisher recommends authors to include contribution statements in the work that specifies the contribution of every author in order to promote transparency. These contributions should be listed at the separate title page.

Examples of such statement(s) are shown below:

• Free text:

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [full name], [full name] and [full name]. The first draft of the manuscript was written by [full name] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Example: CRediT taxonomy:

• Conceptualization: [full name], …; Methodology: [full name], …; Formal analysis and investigation: [full name], …; Writing - original draft preparation: [full name, …]; Writing - review and editing: [full name], …; Funding acquisition: [full name], …; Resources: [full name], …; Supervision: [full name],….

For review articles where discrete statements are less applicable a statement should be included who had the idea for the article, who performed the literature search and data analysis, and who drafted and/or critically revised the work.

For articles that are based primarily on the student’s dissertation or thesis , it is recommended that the student is usually listed as principal author:

A Graduate Student’s Guide to Determining Authorship Credit and Authorship Order, APA Science Student Council 2006

Affiliation

The primary affiliation for each author should be the institution where the majority of their work was done. If an author has subsequently moved, the current address may additionally be stated. Addresses will not be updated or changed after publication of the article.

Changes to authorship

Authors are strongly advised to ensure the correct author group, the Corresponding Author, and the order of authors at submission. Changes of authorship by adding or deleting authors, and/or changes in Corresponding Author, and/or changes in the sequence of authors are not accepted after acceptance of a manuscript.

• Please note that author names will be published exactly as they appear on the accepted submission!

Please make sure that the names of all authors are present and correctly spelled, and that addresses and affiliations are current.

Adding and/or deleting authors at revision stage are generally not permitted, but in some cases it may be warranted. Reasons for these changes in authorship should be explained. Approval of the change during revision is at the discretion of the Editor-in-Chief. Please note that journals may have individual policies on adding and/or deleting authors during revision stage.

Author identification

Authors are recommended to use their ORCID ID when submitting an article for consideration or acquire an ORCID ID via the submission process.

Deceased or incapacitated authors

For cases in which a co-author dies or is incapacitated during the writing, submission, or peer-review process, and the co-authors feel it is appropriate to include the author, co-authors should obtain approval from a (legal) representative which could be a direct relative.

Authorship issues or disputes

In the case of an authorship dispute during peer review or after acceptance and publication, the Journal will not be in a position to investigate or adjudicate. Authors will be asked to resolve the dispute themselves. If they are unable the Journal reserves the right to withdraw a manuscript from the editorial process or in case of a published paper raise the issue with the authors’ institution(s) and abide by its guidelines.

Confidentiality

Authors should treat all communication with the Journal as confidential which includes correspondence with direct representatives from the Journal such as Editors-in-Chief and/or Handling Editors and reviewers’ reports unless explicit consent has been received to share information.

To ensure objectivity and transparency in research and to ensure that accepted principles of ethical and professional conduct have been followed, authors should include information regarding sources of funding, potential conflicts of interest (financial or non-financial), informed consent if the research involved human participants, and a statement on welfare of animals if the research involved animals.

Authors should include the following statements (if applicable) in a separate section entitled “Compliance with Ethical Standards” when submitting a paper:

• Disclosure of potential conflicts of interest
• Research involving Human Participants and/or Animals
• Informed consent

Please note that standards could vary slightly per journal dependent on their peer review policies (i.e. single or double blind peer review) as well as per journal subject discipline. Before submitting your article check the instructions following this section carefully.

The corresponding author should be prepared to collect documentation of compliance with ethical standards and send if requested during peer review or after publication.

The Editors reserve the right to reject manuscripts that do not comply with the above-mentioned guidelines. The author will be held responsible for false statements or failure to fulfill the above-mentioned guidelines.

Authors are requested to disclose interests that are directly or indirectly related to the work submitted for publication. Interests within the last 3 years of beginning the work (conducting the research and preparing the work for submission) should be reported. Interests outside the 3-year time frame must be disclosed if they could reasonably be perceived as influencing the submitted work. Disclosure of interests provides a complete and transparent process and helps readers form their own judgments of potential bias. This is not meant to imply that a financial relationship with an organization that sponsored the research or compensation received for consultancy work is inappropriate.

Editorial Board Members and Editors are required to declare any competing interests and may be excluded from the peer review process if a competing interest exists. In addition, they should exclude themselves from handling manuscripts in cases where there is a competing interest. This may include – but is not limited to – having previously published with one or more of the authors, and sharing the same institution as one or more of the authors. Where an Editor or Editorial Board Member is on the author list we recommend they declare this in the competing interests section on the submitted manuscript. If they are an author or have any other competing interest regarding a specific manuscript, another Editor or member of the Editorial Board will be assigned to assume responsibility for overseeing peer review. These submissions are subject to the exact same review process as any other manuscript. Editorial Board Members are welcome to submit papers to the journal. These submissions are not given any priority over other manuscripts, and Editorial Board Member status has no bearing on editorial consideration.

Interests that should be considered and disclosed but are not limited to the following:

Funding: Research grants from funding agencies (please give the research funder and the grant number) and/or research support (including salaries, equipment, supplies, reimbursement for attending symposia, and other expenses) by organizations that may gain or lose financially through publication of this manuscript.

Employment: Recent (while engaged in the research project), present or anticipated employment by any organization that may gain or lose financially through publication of this manuscript. This includes multiple affiliations (if applicable).

Financial interests: Stocks or shares in companies (including holdings of spouse and/or children) that may gain or lose financially through publication of this manuscript; consultation fees or other forms of remuneration from organizations that may gain or lose financially; patents or patent applications whose value may be affected by publication of this manuscript.

It is difficult to specify a threshold at which a financial interest becomes significant, any such figure is necessarily arbitrary, so one possible practical guideline is the following: "Any undeclared financial interest that could embarrass the author were it to become publicly known after the work was published."

Non-financial interests: In addition, authors are requested to disclose interests that go beyond financial interests that could impart bias on the work submitted for publication such as professional interests, personal relationships or personal beliefs (amongst others). Examples include, but are not limited to: position on editorial board, advisory board or board of directors or other type of management relationships; writing and/or consulting for educational purposes; expert witness; mentoring relations; and so forth.

Primary research articles require a disclosure statement. Review articles present an expert synthesis of evidence and may be treated as an authoritative work on a subject. Review articles therefore require a disclosure statement. Other article types such as editorials, book reviews, comments (amongst others) may, dependent on their content, require a disclosure statement. If you are unclear whether your article type requires a disclosure statement, please contact the Editor-in-Chief.

Please note that, in addition to the above requirements, funding information (given that funding is a potential competing interest (as mentioned above)) needs to be disclosed upon submission of the manuscript in the peer review system. This information will automatically be added to the Record of CrossMark, however it is not added to the manuscript itself. Under ‘summary of requirements’ (see below) funding information should be included in the ‘ Declarations ’ section.

Summary of requirements

The above should be summarized in a statement and placed in a ‘Declarations’ section before the reference list under a heading of ‘Funding’ and/or ‘Competing interests’. Other declarations include Ethics approval, Consent, Data, Material and/or Code availability and Authors’ contribution statements.

Please see the various examples of wording below and revise/customize the sample statements according to your own needs.

When all authors have the same (or no) conflicts and/or funding it is sufficient to use one blanket statement.

Examples of statements to be used when funding has been received:

• Partial financial support was received from [...]
• The research leading to these results received funding from […] under Grant Agreement No[…].
• This study was funded by […]
• This work was supported by […] (Grant numbers […] and […]

Examples of statements to be used when there is no funding:

• The authors did not receive support from any organization for the submitted work.
• No funding was received to assist with the preparation of this manuscript.
• No funding was received for conducting this study.
• No funds, grants, or other support was received.

Examples of statements to be used when there are interests to declare:

Non-financial interests: Author C is an unpaid member of committee Z.

Non-financial interests: Author A is on the board of directors of Y and receives no compensation as member of the board of directors.

Non-financial interests: none.

Non-financial interests: Author D has served on advisory boards for Company M, Company N and Company O.

Examples of statements to be used when authors have nothing to declare:

• The authors have no relevant financial or non-financial interests to disclose.
• The authors have no competing interests to declare that are relevant to the content of this article.
• All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.
• The authors have no financial or proprietary interests in any material discussed in this article.

Authors are responsible for correctness of the statements provided in the manuscript. See also Authorship Principles. The Editor-in-Chief reserves the right to reject submissions that do not meet the guidelines described in this section.

Upon acceptance, your article will be exported to Production to undergo typesetting. Shortly after this you will receive two e-mails. One contains a request to confirm your affiliation, choose the publishing model for your article, as well as to arrange rights and payment of any associated publication cost. A second e-mail containing a link to your article’s proofs will be sent once typesetting is completed.

Article publishing agreement

Depending on the ownership of the journal and its policies, you will either grant the Publisher an exclusive licence to publish the article or will be asked to transfer copyright of the article to the Publisher.

Offprints can be ordered by the corresponding author.

Color illustrations

Online publication of color illustrations is free of charge. For color in the print version, authors will be expected to make a contribution towards the extra costs.

Proof reading

The purpose of the proof is to check for typesetting or conversion errors and the completeness and accuracy of the text, tables and figures. Substantial changes in content, e.g., new results, corrected values, title and authorship, are not allowed without the approval of the Editor.

After online publication, further changes can only be made in the form of an Erratum, which will be hyperlinked to the article.

Online First

The article will be published online after receipt of the corrected proofs. This is the official first publication citable with the DOI. After release of the printed version, the paper can also be cited by issue and page numbers.

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*) Within the first three years of publication. Springer Nature hybrid journal OA impact analysis, 2018.

Funding and Support pages

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