Showing papers in "Journal of Physics A in 2004"
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.
Abstract: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.
2,119 citations
TL;DR: In this article, the exceptional points associated with non-Hermitian operators are investigated and the specific characteristics of the eigenfunctions at the exceptional point are worked out in the domain of real parameters.
Abstract: Exceptional points associated with non-Hermitian operators, i.e. operators being non-Hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values. These and other results are exemplified by a classical problem leading to exceptional points of a non-Hermitian matrix.
417 citations
TL;DR: In this article, the authors review the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces, and present a summary of new improvements to the proximity force approximation and a synopsis of the current experimental situation.
Abstract: The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of δ-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir–Polder forces. A great deal of attention is given to the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces. A summary of new improvements to the proximity force approximation is given, followed by a synopsis of the current experimental situation. New results on Casimir self-stress are reported, again based on δ-function potentials. Progress in understanding divergences in the self-stress of dielectric bodies is described, in particular the status of a continuing calculation of the self-stress of a dielectric cylinder. Casimir effects for solitons, and the status of the so-called dynamical Casimir effect, are summarized. The possibilities of understanding dark energy, strongly constrained by both cosmological and terrestrial experiments, in terms of quantum fluctuations are discussed. Throughout, the centrality of quantum vacuum energy in fundamental physics is emphasized.
372 citations
TL;DR: In this article, the complete polytope of Bell inequalities for two particles with small numbers of possible measurements and outcomes was investigated, and it was shown that there are very few relevant inequivalent inequalities for small numbers.
Abstract: We computationally investigate the complete polytope of Bell inequalities for two particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard NP problem. Despite this, we find that there are very few relevant inequivalent inequalities for small numbers. For example, in the case with three possible 2-outcome measurements on each particle, there is just one new inequality. We describe mixed 2-qubit states which violate this inequality but not the CHSH. The new inequality also illustrates a sharing of bi-partite non-locality between three qubits: something not seen using the CHSH inequality. It also inspires us to discover a class of Bell inequalities with m possible n-outcome measurements on each particle.
369 citations
TL;DR: In this paper, the authors provide an overview of the theory and practice of continuous and discrete wavelet transforms and their application in fluid, engineering, medicine and miscellaneous areas, including machining, materials, dynamics and information engineering.
Abstract: This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies' wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author's own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.
323 citations
TL;DR: In this article, a canonical orthonormal basis for non-Hermitian Hamiltonians is introduced, in which a previously introduced unitary mapping of H to a Hermitian H takes a simple form and is used to construct the observables of the quantum mechanics based on H.
Abstract: For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables Oα of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian quantization scheme that relates the latter to the ordinary classical position and momentum observables. These allow us to address the problem of determining the conserved probability density and the underlying classical system for pseudo-Hermitian and in particular PT-symmetric quantum systems. As a concrete example we construct the Hermitian Hamiltonian h, the physical observables Oα, the localized states and the conserved probability density for the non-Hermitian PT-symmetric square well. We achieve this by employing an appropriate perturbation scheme. For this system, we conduct a comprehensive study of both the kinematical and dynamical effects of the non-Hermiticity of the Hamiltonian on various physical quantities. In particular, we show that these effects are quantum mechanical in nature and diminish in the classical limit. Our results provide an objective assessment of the physical aspects of PT-symmetric quantum mechanics and clarify its relationship with both conventional quantum mechanics and classical mechanics.
323 citations
TL;DR: In this paper, the continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtaining a bound which is independent of the dimension of the second party was proved.
Abstract: We prove continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove the continuity of squashed entanglement.
298 citations
TL;DR: In this paper, the authors present a detailed review of the basic concepts of decoherence in quantum open systems and their application in quantum information processing and quantum quantum physics, including the role of quantum chaos and quantum information in the brain.
Abstract: In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.
273 citations
TL;DR: In this article, the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network were derived for regular lattices in one, two and three dimensions under various boundary conditions.
Abstract: The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Mobius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.
272 citations
TL;DR: This book by Nino Boccara presents a compilation of model systems commonly termed as `complex' and starts with a definition of the systems under consideration and how to build up a model to describe the complex dynamics.
Abstract: This book by Nino Boccara presents a compilation of model systems commonly termed as `complex'. It starts with a definition of the systems under consideration and how to build up a model to describe the complex dynamics. The subsequent chapters are devoted to various categories of mean-field type models (differential and recurrence equations, chaos) and of agent-based models (cellular automata, networks and power-law distributions). Each chapter is supplemented by a number of exercises and their solutions. The table of contents looks a little arbitrary but the author took the most prominent model systems investigated over the years (and up until now there has been no unified theory covering the various aspects of complex dynamics). The model systems are explained by looking at a number of applications in various fields. The book is written as a textbook for interested students as well as serving as a compehensive reference for experts. It is an ideal source for topics to be presented in a lecture on dynamics of complex systems. This is the first book on this `wide' topic and I have long awaited such a book (in fact I planned to write it myself but this is much better than I could ever have written it!). Only section 6 on cellular automata is a little too limited to the author's point of view and one would have expected more about the famous Domany--Kinzel model (and more accurate citation!). In my opinion this is one of the best textbooks published during the last decade and even experts can learn a lot from it. Hopefully there will be an actualization after, say, five years since this field is growing so quickly. The price is too high for students but this, unfortunately, is the normal case today. Nevertheless I think it will be a great success!
268 citations
TL;DR: In this article, the authors show that there exist intimate connections between three unconventional Schrodinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space.
Abstract: We show that there exist some intimate connections between three unconventional Schrodinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space. This occurs whenever a specific relation between the deforming function, the position-dependent mass and the (diagonal) metric tensor holds true. We illustrate these three equivalent approaches by considering a new Coulomb problem and solving it by means of supersymmetric quantum mechanical and shape invariance techniques. We show that in contrast with the conventional Coulomb problem, the new one gives rise to only a finite number of bound states.
TL;DR: The progress of the factorization method since the 1935 work of Dirac is briefly reviewed in this article, where the authors suggest that factorization seems an autonomous "driving force", offering substantial support to the present day Darboux and Backlund approaches.
Abstract: The progress of the factorization method since the 1935 work of Dirac is briefly reviewed. Though linked with older mathematical theories the factorization seems an autonomous 'driving force', offering substantial support to the present day Darboux and Backlund approaches.
TL;DR: In this article, the existence of a global optimization potential function has been shown to be possible by using a dynamical structure built into a stochastic differential equation (SDE).
Abstract: There is a whole range of emergent phenomena in a complex network such as robustness, adaptiveness, multiple-equilibrium, hysteresis, oscillation and feedback. Those non-equilibrium behaviours can often be described by a set of stochastic differential equations. One persistent important question is the existence of a potential function. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. We present an explicit construction procedure to obtain the potential and relevant quantities. In the procedure no reference to the Fokker–Planck equation is needed. The availability of the potential suggests that powerful statistical mechanics tools can be used in nonequilibrium situations.
TL;DR: In this article, a multiple integral representation for a generating function of the σz-σz correlation functions of the spin- XXZ chain at finite temperature and finite, longitudinal magnetic field was derived.
Abstract: We derive a novel multiple integral representation for a generating function of the σz–σz correlation functions of the spin- XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.
TL;DR: In this paper, the integrable open XX quantum spin chain with non-diagonal boundary terms was considered and an exact inversion identity was derived, by which the eigenvalues of the transfer matrix and the Bethe ansatz equations were obtained.
Abstract: We consider the integrable open XX quantum spin chain with non-diagonal boundary terms. We derive an exact inversion identity, by which we obtain the eigenvalues of the transfer matrix and the Bethe ansatz equations. For generic values of the boundary parameters, the Bethe ansatz solution is formulated in terms of the Jacobian elliptic functions.
TL;DR: In this paper, the authors point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined.
Abstract: We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined-i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.
TL;DR: In this paper, a real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale.
Abstract: A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically.
TL;DR: The eigenvalues of the random density matrices are analysed and the eigenvalue distribution for the Bures ensemble is derived, which is shown to be broader then the quarter-circle distribution characteristic of the Hilbert–Schmidt ensemble.
Abstract: Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analysed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter-circle distribution characteristic of the Hilbert–Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.
TL;DR: In this paper, the authors used the smaller alignment index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows, based on the different behaviour of the SALI for the two cases: the index fluctuates around non-zero values for ordered orbits, while it tends rapidly to zero for chaotic orbits.
Abstract: We use the smaller alignment index (SALI) to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian flows This distinction is based on the different behaviour of the SALI for the two cases: the index fluctuates around non-zero values for ordered orbits, while it tends rapidly to zero for chaotic orbits We present a detailed study of SALI’s behaviour for chaotic orbits and show that in this case the SALI exponentially converges to zero, following a time rate depending on the difference of the two largest Lyapunov exponents σ1 ,σ 2 ie SALI ∝ e −(σ
TL;DR: In this article, the UV finite quantum field theory on even-dimensional non-commutative spacetime is formulated using coordinate coherent states, and the 2D space is foliated into families of orthogonal, non-commodity, two planes.
Abstract: Ultraviolet finite quantum field theory on even-dimensional noncommutative spacetime is formulated using coordinate coherent states. 2D spacetime is foliated into families of orthogonal, noncommutative, two planes. Lorentz invariance is recovered if one imposes a single noncommutative parameter θ in the theory. Unitarity is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.
TL;DR: In this article, the spatial rock-scissors-paper game is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site.
Abstract: The spatial rock-scissors-paper game (or cyclic Lotka–Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.
TL;DR: In this paper, the authors review the canonical theory for perfect fluids in Euler's and Lagrange's formulations, which is related to a description of extended structures in higher dimensions, including internal symmetry and supersymmetry degrees of freedom.
Abstract: We review the canonical theory for perfect fluids in Euler's and Lagrange's formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern–Simons terms (= vortex or magnetic helicity).
TL;DR: In this article, the authors performed group classification in a class of variable coefficient (1 + 1)-dimensional nonlinear diffusion?convection equations of the general form f(x)ut = (D(u)ux)x + K(u)-ux.
Abstract: Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient (1 + 1)-dimensional nonlinear diffusion?convection equations of the general form f(x)ut = (D(u)ux)x + K(u)ux. We obtain new interesting cases of such equations with the density f localized in space, which have non-trivial invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local transformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.
TL;DR: In this article, the authors explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory.
Abstract: In this paper we continue to explore the notion of Rota–Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analysed in terms of complete filtered Rota–Baxter algebras.
TL;DR: In this article, the authors investigated the reality of exact bound states of complex and PT-symmetric non-Hermitian exponential-type generalized Hulthen potentials.
Abstract: We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The Klein–Gordon equation has been solved by using the Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. In many cases of interest, negative and positive energy states have been discussed for different types of complex potentials.
TL;DR: In this article, the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions is studied and the steady state of the model is intimately related to the Askey-Wilson polynomials.
Abstract: We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of the model is intimately related to the Askey–Wilson polynomials. The partition function and the n-point functions are obtained in the integral form with four boundary parameters. The thermodynamic current is evaluated to confirm the conjectured phase diagram.
TL;DR: In this paper, a hierarchy of generalized Toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations, and it is shown that the hierarchy possesses a bi-Hamiltonian structure and a hereditary recursion operator.
Abstract: Starting from a modified Toda spectral problem, a hierarchy of generalized Toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations. It is shown that the hierarchy possesses a bi-Hamiltonian structure and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. Two cases of the involved constants present two specific integrable sub-hierarchies, one of which is exactly the Toda lattice hierarchy.
TL;DR: In this article, two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system and the experimental results perfectly match the mathematical predictions at the exceptional point.
Abstract: Two damped coupled oscillators have been used to demonstrate the occurrence of exceptional points in a purely classical system. The implementation was achieved with electronic circuits in the kHz-range. The experimental results perfectly match the mathematical predictions at the exceptional point. A discussion about the universal occurrence of exceptional points—connecting dissipation with spatial orientation—concludes this paper.
TL;DR: In this article, the authors discuss a recently proposed asymptotic iteration method for eigenvalue problems and analyse its rate of convergence, the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas.
Abstract: We discuss a recently proposed asymptotic iteration method for eigenvalue problems. We analyse its rate of convergence, the use of adjustable parameters to improve it and the relationship with an alternative method based on the same ideas.
TL;DR: An analytical procedure is provided which leads to a system of (n − 2)2 polynomial equations whose solutions give the parametrization of the complex n × n Hadamard matrices.
Abstract: In this paper we provide an analytical procedure which leads to a system of (n − 2)2 polynomial equations whose solutions give the parametrization of the complex n × n Hadamard matrices. It is shown that in general the Hadamard matrices depend on a number of arbitrary phases and a lower bound for this number is given. The moduli equations define interesting geometrical objects whose study will shed light on the parametrization of the Hadamard matrices, as well as on some interesting geometrical varieties defined by them.