Journal of Physics A: Mathematical and Theoretical

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Journal of Physics A: Mathematical and Theoretical

Reporting on the mathematical structures that describe the physical world and on the analytical, computational and numerical methods for exploring these structures.

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Issue in progress

Editorial & news

We are making a call for contributions to a special issue on quantum coherence. Guest-edited by Eric Chitambar, Xiongfeng Ma and Alexander Streltsov, this special issue on quantum coherence will aim to advance our understanding on how coherence functions as a resource in various quantum information processing tasks. You can read more here.

We are making a call for contributions to a special issue dedicated to fifty years of the Toda lattice. Guest-edited by Vladimir Bazhanov, Patrick Dorey, Kenji Kajiwara and Kanehisa Takasaki, the issue will collect research papers on latest developments on the Toda lattice and its various generalizations, and topics where the Toda lattice is used as a substantial ingredient. You can read more here.

Journal of Physics A: Mathematical and Theoretical offers an accepted manuscript service, meaning your research can be downloaded and cited within twenty four hours of acceptance. All articles accepted for publication in Journal of Physics A: Mathematical and Theoretical will benefit from this service, however, authors are able to opt-out during the conformity process should they want to. For further information on the benefits of our accepted manuscript service, visit iopscience.org/accepted-manuscripts, or contact [email protected].

We are pleased to announce that we have appointed two fresh Section Editors for the Mathematical Physics section of the journal. Patrick Dorey and Tomohiro Sasamoto are our fresh Editors. We welcome submissions to the section.

To mark the 50th volume of Journal of Physics A in 2017, we present a collection of commentaries on some of the most influential papers published in the journal.

We are very pleased to present the Journal of Physics A Highlights collection for 2016. This collection showcases some of the excellent papers we published in 2016. All articles featured are free to read until the end of December 2017.

M V Berry et al two thousand eleven J. Phys. A: Math. Theor. 44 four hundred ninety two thousand one

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

This topical review article gives an overview of the interplay inbetween quantum information theory and thermodynamics of quantum systems. We concentrate 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.

Xianfei Qi et al two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred eighty five thousand three hundred one

Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz et al (2014 Phys. Rev. Lett. 113 140401) introduced a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a fresh valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure, coherence concurrence, fulfills all the requirements dictated by the resource theory of quantum coherence measures. Moreover, strong links inbetween the resource frameworks of coherence concurrence and entanglement concurrence is derived, which shows that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. Our work provides a clear quantitative and operational connection inbetween coherence and entanglement based on two kinds of concurrence. This fresh coherence measure, coherence concurrence, may also be beneficial to the examine of quantum coherence.

Ewa Gudowska-Nowak et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty thousand three hundred one

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a finish characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The criterion is voiced in terms of a norm arising from anti-diagonal entries. We compute this norm in several cases, so that we get criteria with which we can determine the separability by routine computations.

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of complicated matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for complicated matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly ordinary. We then demonstrate that this elementary formula should be valid for all matrices and operators.

Jacob C Bridgeman and Christopher T Chubb two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred twenty three thousand one

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the explore of condensed matter systems. Tensor networks have proven an significant instrument 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, albeit 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.

Gregory Berkolaiko et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred sixty five thousand two hundred one

We derive a number of upper and lower bounds for the very first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be eliminated to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a fresh variational proof. On quantum graphs, the corresponding roped generalizes a latest result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and permit us to identify the minimizers.

Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are ‘asymptotically correct`, i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve latest results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a finish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and showcase accomplish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system sated by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard technics of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we showcase that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz technologies. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

J De Nardis et al two thousand fifteen J. Phys. A: Math. Theor. 48 43FT01

We showcase, using the quench activity treatment (Caux and Essler two thousand thirteen Phys. Rev. Lett. 110 257203), that the entire post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient This function can be extracted from the thermodynamically leading part of the overlaps inbetween the eigenstates of the model and the initial state. For a generic global quench the form of in the low momentum limit directly gives the exponent for the power law decay to the effective stable state. As an example we compute the time evolution of the static density–density correlation in the interacting Lieb–Liniger gas after a quench from a Bose–Einstein condensate. This shows an treatment to equilibrium with power law t −Three which turns out to be independent of the post-quench interaction and of the considered observable.

Tomaž Prosen two thousand fifteen J. Phys. A: Math. Theor. 48 three hundred seventy three thousand one

We review latest progress on constructing non-equilibrium constant state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation channels affixed to the chain`s completes. We discuss explicit solutions in three different classes of quantum chains, specifically, the paradigmatic (anisotropic) Heisenberg spin- chain, the Fermi–Hubbard chain, and the Lai–Sutherland spin-1 chain, and discuss universal concepts which characterize these solutions, such as matrix product ansatz and a more structured walking graph state ansatz. The central theme is the connection inbetween the matrix product form of nonequilibrium states and the integrability structures of the bulk Hamiltonian, such as the Lax operators and the Yang–Baxter equation. However, there is a remarkable distinction with respect to the conventional quantum inverse scattering method, namely addressing nonequilibrium stable state density operators requires non-unitary irreducible representations of Yang–Baxter algebra which are typically of infinite dimensionality. Such constructions result in non-Hermitian, and often also non-diagonalisable families of commuting transfer operators which in turn result in novel conservation laws of the integrable bulk Hamiltonians. For example, in the case of the anisotropic Heisenberg model, quasi-local conserved operators which are odd under spin reversal (or spin roll) can be constructed, whereas the conserved operators stemming from orthodox Hermitian transfer operators (via logarithmic differentiation) are all even under spin reversal.

Angnis Schmidt-May and Mikael von Strauss two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred eighty three thousand one

This review is dedicated to latest progress in the field of classical, interacting, massive spin-2 theories, with a concentrate on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of movement in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity thresholds of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and eventually we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.

Gerardo Adesso et al two thousand sixteen J. Phys. A: Math. Theor. 49 four hundred seventy three thousand one

Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced spectacle of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a decent understanding and characterisation of the frontier inbetween classical and quantum correlations (QCs) in composite states. We concentrate on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

Fei Ye et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred ninety five thousand four hundred one

The relation inbetween braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an suitable dimensional reduction. If the matter act is anomalous, as for chiral fermions, a relation inbetween braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Eventually, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.

Koji Ohkitani two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand five hundred one

We make a refined comparison inbetween the Navier–Stokes equations and their dynamically-scaled Leray equations solely on the basis of their scaling property. Previously it was observed using the vector potentials that they differ only by one drift term (Ohkitani two thousand seventeen J. Phys. A: Math. Theor. 50 045501). The Duhamel principle recasts the equations in path integral forms, which differ by two Maruyama–Girsanov densities. In this brief paper we simplify the concept of quasi-invariance (or, near-invariance) by combining the result with a Cole–Hopf convert and the Feynman–Kac formula. That way, as a multiplicative characterisation we can place those equations just one Maruyama–Girsanov density apart. Furthermore, as an additive characterisation we express the difference in terms of the Malliavin H-derivative.

V Skogvoll and O Liabøtrø two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred one

The composite fermion (CF) formalism produces wave functions that are not always linearly independent. This is especially so in the low angular momentum regime in the lowest Landau level, where a subclass of CF states, known as ordinary states, gives a good description of the low energy spectrum. For the two-component Bose gas, explicit bases avoiding the large number of redundant states have been found. We generalize one of these bases to the M-component Bose gas and prove its validity. We also demonstrate that the numbers of linearly independent plain states for different values of angular momentum are given by coefficients of q-multinomials.

X Z Zhang et al two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred two

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We display that such composite systems have an SS at if the reflection amplitudes and of the two scattering centers please the condition . We also extend the condition to the system with multi-scattering centers. As an application, we construct a plain system to simulate a resonant lasing cavity.

Jens Funke and Stephen S Kudla two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred four thousand one

Mock modular forms are central objects in the latest discoveries of fresh instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers` mock theta functions of type as line integrals in hyperbolic p-space.

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a accomplish characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The criterion is voiced in terms of a norm arising from anti-diagonal entries. We compute this norm in several cases, so that we get criteria with which we can determine the separability by routine computations.

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a accomplish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and demonstrate accomplish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system sated by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of sophisticated matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for sophisticated matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly plain. We then display that this elementary formula should be valid for all matrices and operators.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard technics of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we showcase that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz mechanisms. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

Rouven Frassek two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty five thousand two hundred two

We explore the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification permits us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.

Charlotte Sleight two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty three thousand one

This review is an elaboration of latest results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured duality with free conformal field theories (CFTs). After reviewing the general treatment and establishing the necessary intermediate results, we extract explicit expressions for the finish cubic act on and the quartic self-interaction of the scalar on AdS four for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar vector model. For this purpose devices were developed to evaluate tree-level three-point Witten diagrams involving totally symmetric fields of arbitrary integer spin and mass, and the conformal partial wave expansions of their tree-level four-point Witten diagrams. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.

Andrew R Conway two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifty three thousand one

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper covers the design and implementation of such algorithms.

A host of general technologies for improving efficiency are described. Three fairly different example problems are used for detailed examples: one thousand three hundred twenty four pattern avoiding permutations, three-dimensional polycubes (using a novel treatment), and two-dimensional directed animals. Other examples from the literature are used when suitable to describe applicability of various technologies, but the paper does not attempt to survey all applications.

Claude Godrèche et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred thirty three thousand one

We review latest advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we concentrate on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory` to test the effects of correlations on the record statistics. We begin with the ordinary one-dimensional random walk with symmetric hops (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time inbetween two successive record cracking events. Then we review the results that were obtained for a broad multitude of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of numerous independent random walkers. Eventually, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

Andrei B Klimov et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred twenty three thousand one

We survey some applications of SU(Two) covariant maps to the phase space quantum mechanics of systems with motionless or variable spin. A generalization to SU(Three) symmetry is also shortly discussed in framework of the axiomatic Stratonovich–Weyl formulation.

Michael Assaf and Baruch Meerson two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty three thousand one

Stochasticity can play an significant role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics–such as those determining population extinction, fixation or switching inbetween different states–are presently in a concentrate of attention of statistical physicists. We review latest progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation permits one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and numerous, but also shortly consider populations on heterogeneous networks and spatial populations. The spatial setting also permits one to examine large fluctuations of the speed of biological invasions. Ultimately, we shortly discuss possible directions of future work.

Stephen L Adler two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred ninety five thousand four hundred one

We proceed our investigate of Coleman–Weinberg symmetry violating induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler two thousand fourteen Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We concentrate in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for providing the spin field a mass by the BEH mechanism, and analyze the remaining massless spin fermions, the global chiral symmetries, and the running couplings after symmetry cracking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B− L , and conjecture that the theory runs to an infrared stationary point at which there is a massless gluon with three to −1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric violating of Sp(Four) to SU(Two) subgroups, one of which is the electroweak SU(Two), and the other of which is a ‘technicolor` group that ties the original SU(8) model fermions, which play the role of ‘preons`, into composites. Quarks can emerge as five preon composites and leptons as three preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

2007-present Journal of Physics A: Mathematical and Theoretical

Journal of Physics A: Mathematical and Theoretical

Reporting on the mathematical structures that describe the physical world and on the analytical, computational and numerical methods for exploring these structures.

Latest issue (finish)

Issue in progress

Editorial & news

To mark the 50th volume of Journal of Physics A in 2017, we present a collection of commentaries on some of the most influential papers published in the journal.

M V Berry et al two thousand eleven J. Phys. A: Math. Theor. 44 four hundred ninety two thousand one

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

Xianfei Qi et al two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred eighty five thousand three hundred one

Ewa Gudowska-Nowak et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty thousand three hundred one

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of complicated matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for elaborate matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly plain. We then showcase that this ordinary formula should be valid for all matrices and operators.

Jacob C Bridgeman and Christopher T Chubb two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred twenty three thousand one

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

Gregory Berkolaiko et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred sixty five thousand two hundred one

We derive a number of upper and lower bounds for the very first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be eliminated to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a fresh variational proof. On quantum graphs, the corresponding trussed generalizes a latest result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and permit us to identify the minimizers.

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a finish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and demonstrate finish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system pleased by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard mechanisms of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we display that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz technologies. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

J De Nardis et al two thousand fifteen J. Phys. A: Math. Theor. 48 43FT01

We demonstrate, using the quench activity treatment (Caux and Essler two thousand thirteen Phys. Rev. Lett. 110 257203), that the entire post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient This function can be extracted from the thermodynamically leading part of the overlaps inbetween the eigenstates of the model and the initial state. For a generic global quench the form of in the low momentum limit directly gives the exponent for the power law decay to the effective constant state. As an example we compute the time evolution of the static density–density correlation in the interacting Lieb–Liniger gas after a quench from a Bose–Einstein condensate. This shows an treatment to equilibrium with power law t −Three which turns out to be independent of the post-quench interaction and of the considered observable.

Tomaž Prosen two thousand fifteen J. Phys. A: Math. Theor. 48 three hundred seventy three thousand one

We review latest progress on constructing non-equilibrium stable state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation channels fastened to the chain`s completes. We discuss explicit solutions in three different classes of quantum chains, specifically, the paradigmatic (anisotropic) Heisenberg spin- chain, the Fermi–Hubbard chain, and the Lai–Sutherland spin-1 chain, and discuss universal concepts which characterize these solutions, such as matrix product ansatz and a more structured walking graph state ansatz. The central theme is the connection inbetween the matrix product form of nonequilibrium states and the integrability structures of the bulk Hamiltonian, such as the Lax operators and the Yang–Baxter equation. However, there is a remarkable distinction with respect to the conventional quantum inverse scattering method, namely addressing nonequilibrium stable state density operators requires non-unitary irreducible representations of Yang–Baxter algebra which are typically of infinite dimensionality. Such constructions result in non-Hermitian, and often also non-diagonalisable families of commuting transfer operators which in turn result in novel conservation laws of the integrable bulk Hamiltonians. For example, in the case of the anisotropic Heisenberg model, quasi-local conserved operators which are odd under spin reversal (or spin roll) can be constructed, whereas the conserved operators stemming from orthodox Hermitian transfer operators (via logarithmic differentiation) are all even under spin reversal.

Angnis Schmidt-May and Mikael von Strauss two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred eighty three thousand one

Gerardo Adesso et al two thousand sixteen J. Phys. A: Math. Theor. 49 four hundred seventy three thousand one

Fei Ye et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred ninety five thousand four hundred one

The relation inbetween braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an suitable dimensional reduction. If the matter act is anomalous, as for chiral fermions, a relation inbetween braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Ultimately, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.

Koji Ohkitani two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand five hundred one

V Skogvoll and O Liabøtrø two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred one

The composite fermion (CF) formalism produces wave functions that are not always linearly independent. This is especially so in the low angular momentum regime in the lowest Landau level, where a subclass of CF states, known as ordinary states, gives a good description of the low energy spectrum. For the two-component Bose gas, explicit bases avoiding the large number of redundant states have been found. We generalize one of these bases to the M-component Bose gas and prove its validity. We also display that the numbers of linearly independent elementary states for different values of angular momentum are given by coefficients of q-multinomials.

X Z Zhang et al two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred two

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We display that such composite systems have an SS at if the reflection amplitudes and of the two scattering centers sate the condition . We also extend the condition to the system with multi-scattering centers. As an application, we construct a ordinary system to simulate a resonant lasing cavity.

Jens Funke and Stephen S Kudla two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred four thousand one

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a accomplish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and demonstrate finish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system pleased by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of complicated matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for elaborate matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly ordinary. We then display that this elementary formula should be valid for all matrices and operators.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard technologies of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we display that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz mechanisms. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

Rouven Frassek two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty five thousand two hundred two

We examine the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification permits us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.

Charlotte Sleight two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty three thousand one

This review is an elaboration of latest results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured duality with free conformal field theories (CFTs). After reviewing the general treatment and establishing the necessary intermediate results, we extract explicit expressions for the accomplish cubic act on and the quartic self-interaction of the scalar on AdS four for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar vector model. For this purpose contraptions were developed to evaluate tree-level three-point Witten diagrams involving totally symmetric fields of arbitrary integer spin and mass, and the conformal partial wave expansions of their tree-level four-point Witten diagrams. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.

Andrew R Conway two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifty three thousand one

A host of general technics for improving efficiency are described. Three fairly different example problems are used for detailed examples: one thousand three hundred twenty four pattern avoiding permutations, three-dimensional polycubes (using a novel treatment), and two-dimensional directed animals. Other examples from the literature are used when adequate to describe applicability of various technologies, but the paper does not attempt to survey all applications.

Claude Godrèche et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred thirty three thousand one

We review latest advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we concentrate on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory` to test the effects of correlations on the record statistics. We begin with the elementary one-dimensional random walk with symmetric hops (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time inbetween two successive record violating events. Then we review the results that were obtained for a broad diversity of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of numerous independent random walkers. Ultimately, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

Andrei B Klimov et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred twenty three thousand one

We survey some applications of SU(Two) covariant maps to the phase space quantum mechanics of systems with immobile or variable spin. A generalization to SU(Three) symmetry is also shortly discussed in framework of the axiomatic Stratonovich–Weyl formulation.

Michael Assaf and Baruch Meerson two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty three thousand one

Stochasticity can play an significant role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics–such as those determining population extinction, fixation or switching inbetween different states–are presently in a concentrate of attention of statistical physicists. We review latest progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation permits one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and numerous, but also shortly consider populations on heterogeneous networks and spatial populations. The spatial setting also permits one to probe large fluctuations of the speed of biological invasions. Ultimately, we shortly discuss possible directions of future work.

Stephen L Adler two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred ninety five thousand four hundred one

We proceed our investigate of Coleman–Weinberg symmetry violating induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler two thousand fourteen Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We concentrate in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for providing the spin field a mass by the BEH mechanism, and analyze the remaining massless spin fermions, the global chiral symmetries, and the running couplings after symmetry cracking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B− L , and conjecture that the theory runs to an infrared motionless point at which there is a massless gluon with three to −1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric violating of Sp(Four) to SU(Two) subgroups, one of which is the electroweak SU(Two), and the other of which is a ‘technicolor` group that trusses the original SU(8) model fermions, which play the role of ‘preons`, into composites. Quarks can emerge as five preon composites and leptons as three preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

2007-present Journal of Physics A: Mathematical and Theoretical

Journal of Physics A: Mathematical and Theoretical

Reporting on the mathematical structures that describe the physical world and on the analytical, computational and numerical methods for exploring these structures.

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To mark the 50th volume of Journal of Physics A in 2017, we present a collection of commentaries on some of the most influential papers published in the journal.

M V Berry et al two thousand eleven J. Phys. A: Math. Theor. 44 four hundred ninety two thousand one

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

Xianfei Qi et al two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred eighty five thousand three hundred one

Ewa Gudowska-Nowak et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty thousand three hundred one

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of complicated matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for elaborate matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly elementary. We then display that this elementary formula should be valid for all matrices and operators.

Jacob C Bridgeman and Christopher T Chubb two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred twenty three thousand one

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

Gregory Berkolaiko et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred sixty five thousand two hundred one

We derive a number of upper and lower bounds for the very first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be eliminated to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a fresh variational proof. On quantum graphs, the corresponding strapped generalizes a latest result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and permit us to identify the minimizers.

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a accomplish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and display finish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system sated by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard mechanisms of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we demonstrate that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz mechanisms. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

John Goold et al two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred forty three thousand one

J De Nardis et al two thousand fifteen J. Phys. A: Math. Theor. 48 43FT01

We demonstrate, using the quench act treatment (Caux and Essler two thousand thirteen Phys. Rev. Lett. 110 257203), that the entire post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient This function can be extracted from the thermodynamically leading part of the overlaps inbetween the eigenstates of the model and the initial state. For a generic global quench the form of in the low momentum limit directly gives the exponent for the power law decay to the effective sustained state. As an example we compute the time evolution of the static density–density correlation in the interacting Lieb–Liniger gas after a quench from a Bose–Einstein condensate. This shows an treatment to equilibrium with power law t −Trio which turns out to be independent of the post-quench interaction and of the considered observable.

Tomaž Prosen two thousand fifteen J. Phys. A: Math. Theor. 48 three hundred seventy three thousand one

We review latest progress on constructing non-equilibrium constant state density operators of boundary driven locally interacting quantum chains, where driving is implemented via Markovian dissipation channels affixed to the chain`s finishes. We discuss explicit solutions in three different classes of quantum chains, specifically, the paradigmatic (anisotropic) Heisenberg spin- chain, the Fermi–Hubbard chain, and the Lai–Sutherland spin-1 chain, and discuss universal concepts which characterize these solutions, such as matrix product ansatz and a more structured walking graph state ansatz. The central theme is the connection inbetween the matrix product form of nonequilibrium states and the integrability structures of the bulk Hamiltonian, such as the Lax operators and the Yang–Baxter equation. However, there is a remarkable distinction with respect to the conventional quantum inverse scattering method, namely addressing nonequilibrium stable state density operators requires non-unitary irreducible representations of Yang–Baxter algebra which are typically of infinite dimensionality. Such constructions result in non-Hermitian, and often also non-diagonalisable families of commuting transfer operators which in turn result in novel conservation laws of the integrable bulk Hamiltonians. For example, in the case of the anisotropic Heisenberg model, quasi-local conserved operators which are odd under spin reversal (or spin roll) can be constructed, whereas the conserved operators stemming from orthodox Hermitian transfer operators (via logarithmic differentiation) are all even under spin reversal.

Angnis Schmidt-May and Mikael von Strauss two thousand sixteen J. Phys. A: Math. Theor. 49 one hundred eighty three thousand one

This review is dedicated to latest progress in the field of classical, interacting, massive spin-2 theories, with a concentrate on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of movability in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity thresholds of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and eventually we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.

Gerardo Adesso et al two thousand sixteen J. Phys. A: Math. Theor. 49 four hundred seventy three thousand one

Fei Ye et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred ninety five thousand four hundred one

The relation inbetween braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern–Simons statistical transmutation in gauge invariant form with an suitable dimensional reduction. If the matter activity is anomalous, as for chiral fermions, a relation inbetween braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Eventually, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.

Koji Ohkitani two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand five hundred one

V Skogvoll and O Liabøtrø two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred one

The composite fermion (CF) formalism produces wave functions that are not always linearly independent. This is especially so in the low angular momentum regime in the lowest Landau level, where a subclass of CF states, known as plain states, gives a good description of the low energy spectrum. For the two-component Bose gas, explicit bases avoiding the large number of redundant states have been found. We generalize one of these bases to the M-component Bose gas and prove its validity. We also display that the numbers of linearly independent elementary states for different values of angular momentum are given by coefficients of q-multinomials.

X Z Zhang et al two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred five thousand three hundred two

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We showcase that such composite systems have an SS at if the reflection amplitudes and of the two scattering centers sate the condition . We also extend the condition to the system with multi-scattering centers. As an application, we construct a plain system to simulate a resonant lasing cavity.

Jens Funke and Stephen S Kudla two thousand seventeen J. Phys. A: Math. Theor. 50 four hundred four thousand one

Lin Chen et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred forty five thousand three hundred three

P Antonelli and P Marcati two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifteen thousand one hundred one

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by N quantum oscillators (‘knots`) connected by a quantum network where the wavefunction at each knot is distributed over quantum channels to all other connected knots. It leads to a system of Schrödinger equations coupled by nonlinear self-interacting potentials given by their correlations. We give a finish picture of synchronization results, given on the relative size of the natural frequency and the coupling constant, for two non-identical oscillators and showcase finish phase synchronization for arbitrary identical oscillators. Our results are mainly based on the analysis of the ODE system pleased by the correlations and on the introduction of a quantum order parameter, which is analogous to the one defined by Kuramoto in the classical model. As a consequence of the previous results, we obtain the synchronization of the probability and the current densities defined via the Madelung transformations.

D L Foulis two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand two hundred four

We derive a closed formula for the Baker–Campbell–Hausdorff series expansion in the case of elaborate matrices. For arbitrary matrices A and B, and a matrix Z such that , our result voices Z as a linear combination of A and B, their commutator , and the identity matrix I. The coefficients in this linear combination are functions of the traces and determinants of A and B, and the trace of their product. The derivation proceeds purely via algebraic manipulations of the given matrices and their products, making use of relations developed here, based on the Cayley–Hamilton theorem, as well as a characterization of the consequences of and/or its determinant being zero or otherwise. As a corollary of our main result we also derive a closed formula for the Zassenhaus expansion. We apply our results to several special cases, most notably the parametrization of the product of two matrices and a verification of the latest result of Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) for sophisticated matrices, in this latter case deriving also the related Zassenhaus formula which turns out to be fairly elementary. We then demonstrate that this plain formula should be valid for all matrices and operators.

Calan Appadu et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred five thousand four hundred one

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current–current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard technologies of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an treatment of Faddeev and Reshetikhin, we display that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz technologies. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.

Rouven Frassek two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty five thousand two hundred two

Charlotte Sleight two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred eighty three thousand one

This review is an elaboration of latest results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured duality with free conformal field theories (CFTs). After reviewing the general treatment and establishing the necessary intermediate results, we extract explicit expressions for the accomplish cubic act on and the quartic self-interaction of the scalar on AdS four for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar vector model. For this purpose instruments were developed to evaluate tree-level three-point Witten diagrams involving totally symmetric fields of arbitrary integer spin and mass, and the conformal partial wave expansions of their tree-level four-point Witten diagrams. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.

Andrew R Conway two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred fifty three thousand one

A host of general mechanisms for improving efficiency are described. Three fairly different example problems are used for detailed examples: one thousand three hundred twenty four pattern avoiding permutations, three-dimensional polycubes (using a novel treatment), and two-dimensional directed animals. Other examples from the literature are used when suitable to describe applicability of various technologies, but the paper does not attempt to survey all applications.

Claude Godrèche et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred thirty three thousand one

We review latest advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we concentrate on random walks. During the last few years, it was indeed realized that random walks are a very useful ‘laboratory` to test the effects of correlations on the record statistics. We embark with the plain one-dimensional random walk with symmetric leaps (both continuous and discrete) and discuss in detail the statistics of the number of records, as well as of the ages of the records, i.e. the lapses of time inbetween two successive record violating events. Then we review the results that were obtained for a broad multitude of random walk models, including random walks with a linear drift, continuous time random walks, constrained random walks (like the random walk bridge) and the case of numerous independent random walkers. Ultimately, we discuss further observables related to records, like the record increments, as well as some questions raised by physical applications of record statistics, like the effects of measurement error and noise.

Andrei B Klimov et al two thousand seventeen J. Phys. A: Math. Theor. 50 three hundred twenty three thousand one

We survey some applications of SU(Two) covariant maps to the phase space quantum mechanics of systems with immovable or variable spin. A generalization to SU(Trio) symmetry is also shortly discussed in framework of the axiomatic Stratonovich–Weyl formulation.

Michael Assaf and Baruch Meerson two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred sixty three thousand one

Stochasticity can play an significant role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and people. Large deviations in stochastic population dynamics–such as those determining population extinction, fixation or switching inbetween different states–are presently in a concentrate of attention of statistical physicists. We review latest progress in applying different variants of dissipative WKB approximation (after Wentzel, Kramers and Brillouin) to this class of problems. The WKB approximation permits one to evaluate the mean time and/or probability of population extinction, fixation and switches resulting from either intrinsic (demographic) noise, or a combination of the demographic noise and environmental variations, deterministic or random. We mostly cover well-mixed populations, single and numerous, but also shortly consider populations on heterogeneous networks and spatial populations. The spatial setting also permits one to explore large fluctuations of the speed of biological invasions. Ultimately, we shortly discuss possible directions of future work.

Stephen L Adler two thousand seventeen J. Phys. A: Math. Theor. 50 two hundred ninety five thousand four hundred one

We proceed our investigate of Coleman–Weinberg symmetry violating induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler two thousand fourteen Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We concentrate in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for providing the spin field a mass by the BEH mechanism, and analyze the remaining massless spin fermions, the global chiral symmetries, and the running couplings after symmetry violating. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1) B− L , and conjecture that the theory runs to an infrared immobilized point at which there is a massless gluon with three to −1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric cracking of Sp(Four) to SU(Two) subgroups, one of which is the electroweak SU(Two), and the other of which is a ‘technicolor` group that ties the original SU(8) model fermions, which play the role of ‘preons`, into composites. Quarks can emerge as five preon composites and leptons as three preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

2007-present Journal of Physics A: Mathematical and Theoretical