We study the dynamics of the separation (gap) between a pair of interacting run and tumble particles moving in one dimension in the presence of additional thermal noise. On a ring geometry the distribution of the gap approaches a steady state. We analytically compute this distribution and find that this is exponentially localised in space, in contrast to the ‘jammed’ configuration, seen earlier in

We study matrix integration over the classical Lie groups U ( N ), Sp (2 N ), SO (2 N ) and SO (2 N + 1), using symmetric function theory and the equivalent formulation in terms of determinants and minors of Toeplitz ± Hankel matrices. We establish a number of factorizations and expansions for such integrals, also with insertions of irreducible characters. As a specific example, we compute both at

We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, arXiv:1104.1004 , for the reduced density of states of two disjoint intervals with lattice sites P = {1, 2, …, m } ∪ {2 m + 1, 2 m + 2, …, 3 m }, which applies to this model. As a first step in the asymptotic analysis of this system, we consider

In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg–de Vries-type equations of the form ##IMG## [http://ej.iop.org/images/1751-8121/53/34/345703/aab9da3ieqn1.gif] {${u}_{t}+{\alpha }_{n}\enspace {u}^{n}\enspace {u}_{x}+{\beta }_{m}{\left({D}_{m}\left\{u\right\}\right)}_{x}=0,{D}_{m}\left\{u\right\}=-\vert k{\vert }^{m}\enspace u\left(k\right)$}

The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for constructing efficient sensing networks, is that of the role of inter-sensor correlations in the simultaneous estimation of multiple linear functions, where the latter

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In a previous study we developed a mean-field theory of dynamical transitions for the totally-asymmetric simple-exclusion process with open boundaries and Langmuir kinetics, in the so-called balanced regime, characterized by equal binding and unbinding rates. Here we show that simply including the possibility of unbalanced rates gives rise to an unexpectedly richer dynamical phase diagram. In particular

Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different k , the amount of k -partite correlations

The experimental advance on light–matter interaction into strong couplings has invalidated the Jaynes–Cummings model and brought the quantum Rabi model (QRM) to more relevance. The QRM only involves linear coupling via a single -photon process (SPP), while the nonlinear two -photon process (TPP) is weaker and conventionally neglected. However, we find a contrary trend that enhancing the linear coupling

Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor N of an RCFT and the quadratic residues modulo N play an important role in the computation and classification of Galois permutations. We establish a field correspondence

We derive the thermodynamic Bethe ansatz (TBA) equations for the Schrödinger equation with an arbitrary polynomial potential and a regular singular (simple and double pole) term. The TBA equations provide a non-trivial generalization of the ODE/IM correspondence and also give a solution for the Riemann–Hilbert problem in the exact WKB method. We study the TBA equations in detail for the linear and

The analysis of fluctuations generated by a thermal reservoir has produced many results throughout the history of science, ranging from the verification of the atomic hypothesis, running through critical phenomena to the most recent advances in the description of non-equilibrium thermodynamic processes. Motivated by recent theoretical and experimental works, we analyze the non-equilibrium and equilibrium

Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the target is small (the narrow escape problem) or if the searcher must escape a potential well. However, many systems depend on the first time a searcher finds the

Compressed sensing allows for the acquisition of compressible signals with a small number of measurements. In experimental settings, the sensing process corresponding to the hardware implementation is not always perfectly known and may require a calibration. To this end, blind calibration proposes to perform at the same time the calibration and the compressed sensing. Schülke and collaborators suggested

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to a universality class of chaotic systems where this numerical coincidence effect can be described by mapping it to a first-passage process. Our results are applicable

For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state , i.e. a statistical distribution of configurations observed along a time lattice. Such a time state is defined with respect to a particular equilibrium state that is invariant under space and time translations

In recent work on superconformal quantum field theories, Razamat arrived at elliptic kernel identities of a new and striking character: they relate solely to the root systems A 2 and A 3 and have no coupling type parameters, Razamat S S (2019 Lett. Math. Phys. 109 1377–95). The pertinent two- and three-variable Hamiltonians are analytic difference operators and the kernel functions are built from the

We study the entanglement structure of symmetry-protected topological (SPT) phases from an operational point of view by considering entanglement distillation in the presence of symmetries. We demonstrate that non-trivial SPT phases in one-dimension necessarily contain some entanglement which is inaccessible if the symmetry is enforced. More precisely, we consider the setting of local operations and

We classify the Lie point symmetries of a system of nonlinearly coupled complex Ginzburg–Landau equations with time and space dependent potentials and nonlinearities. New families of systems with exact solutions and conservation laws are identified. When there is only space dependence, the system can be reduced to a set of ordinary differential equations for the amplitude and phase components, for

The Bloch–Torrey equation governs the evolution of the transverse magnetization in diffusion magnetic resonance imaging, where two mechanisms are at play: diffusion of spins (Laplacian term) and their precession in a magnetic field gradient (imaginary potential term). In this paper, we study this equation in a periodic medium: a unit cell repeated over the nodes of a lattice. Although the gradient

We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials U ( x ) ∼ x m , m = 2 n ⩾ 2. This is paralleled by a transformation of each m th diffusion generator L = D Δ + b ( x )∇, and likewise the related Fokker–Planck operator L * = D Δ − ∇[ b ( x ) ⋅], into the affiliated Schrödinger one ##IMG## [http://ej

We derive a semiclassical nonequilibrium work identity by applying the Wigner–Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us to extend the concept of work to the leading order in ℏ . We propose a geometric interpretation of this semiclassical Jarzynski relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable

Machine learning methods have had spectacular success on numerous problems. Here we show that a prominent class of learning algorithms—including support vector machines (SVMs)—have a natural interpretation in terms of ecological dynamics. We use these ideas to design new online SVM algorithms that exploit ecological invasions, and benchmark performance using the MNIST dataset. Our work provides a new

We establish a connection between non-Markovianity and negative entropy production rate for various classes of quantum operations. We analyse several aspects of unital and thermal operations in connection with resource theories of purity and thermodynamics. We fully characterize Lindblad operators corresponding to unital operations. We also characterize the Lindblad dynamics for a large class of thermal

For the parametrically driven nonlinear Schrödinger equation, two criteria for the dynamical stability of solitons are presented, using the driving force f ( x , t ) = a exp[2 i K ( t ) x ]. Both criteria are based on the results of a collective coordinate theory. In this theory, the parameters of the 1-soliton solution are allowed to depend on time and a variational approach yields a set of coupled

Creating n perfect clones from m copies of one of N prior known quantum states with minimum failure probability is a long-standing problem. We present a general geometrical form of the sufficient and necessary condition of probabilistic cloning of N known quantum states. With only one equality, we delineate in a parameter space the feasible set for probabilistic cloning of N known quantum states with

We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form of tails at the two neighbouring ends. We analyse kink stability equation in all these cases and show that there is no gap between the zero mode and the beginning of the continuum. Finally, we provide a recipe for obtaining

The analytically exact solutions to the two-photon Rabi–Stark model are given by using the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived. The zeros of the transcendental functions reproduce completely the regular spectra. The first-order quantum phase transitions are also detected by the pole structure of the derived transcendental functions

We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize

We consider a Bose gas in a one-dimensional periodic background formed by generalized delta function potentials with one and two impurities. We investigate the scattering off these impurities and their bound state levels. Besides expected features, we observe a kind of long-range correlation between the bound state levels of two impurities. Further, we define and calculate the vacuum energy of the

In a September 1976 PRL Eguchi and Freund considered two topological invariants: the Pontryagin number ##IMG## [http://ej.iop.org/images/1751-8121/53/30/301001/aab956dieqn1.gif] {$P\sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}R$} and the Euler number ##IMG## [http://ej.iop.org/images/1751-8121/53/30/301001/aab956dieqn2.gif] {$\chi \sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}{R}^{{\ast}}$} and

The main object of this work is to analyse the impacts of fear effect on the dynamics of predator–prey interaction incorporating non linear prey refuge to control the extinction of predator. We have taken a Holling type II functional response in presence of additional food. The positivity and uniform boundedness of solutions have been discussed. The feasibility conditions of all equilibrium points

The phase-separation process of a binary mixture with order-parameter-dependent mobility under shear flow is numerically studied. The ordering is characterized by an alternate stretching and bursting of domains which produce oscillations in the physical observables. The amplitude of such modulations reduce in time when the mobility vanishes in the bulk phase, disfavoring the growth of bubbles coming

We investigate the first law of complexity proposed in Bernamonti et al (2019 Phys. Rev. Lett. 123 081601), i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen’s geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits

We consider the index of a Dirac operator on a compact even dimensional manifold with a domain wall. The latter is defined as a co-dimension one submanifold where the connection jumps. We formulate and prove an analog of the Atiyah–Patodi–Singer theorem that relates the index to the bulk integral of Pontryagin density and η -invariants of auxiliary Dirac operators on the domain wall. Thus the index

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but those in a channel that are moving away from a cavity

We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose

The conditional mutual information (CMI) ##IMG## [http://ej.iop.org/images/1751-8121/53/30/305302/aab93fdieqn1.gif] {$\mathcal{I}\left(A:C\vert B\right)$} quantifies the amount of correlations shared between A and C given B . It therefore functions as a more general quantifier of bipartite correlations in multipartite scenarios, playing an important role in the theory of quantum Markov chains. In this

Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial complexes. Simplicial complexes generalize networks by not only taking pairwise interactions into account, but also taking into account many-body interactions between

We develop an approach for designing complex potentials with two or three coexisting spectral singularities in the spectra of the respective Schrödinger operators. The approach is illustrated with several examples. In addition, we offer a simple recipe to create a second-order spectral singularity by intentionally colliding two simple ones.

We investigate the spectral and eigenstate properties of the quantum superexponential oscillator. Our focus is on the quantum signatures of the recently observed transition of the energy dependent period of the corresponding classical superexponential oscillator. We show that the ground state exhibits a remarkable metamorphosis of decentering, asymmetrical squeezing and the development of a tail. Analyzing

This paper is concerned with the modified Camassa–Holm equation and its Bäcklund transformation. With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent and independent variables, is constructed for the modified Camassa–Holm equation. The related nonlinear superposition formula is worked out and applications

The dynamics of a probe M5-brane, embedded as a hypersurface in eleven-dimensional Minkowski spacetime, is described by a six-dimensional world-volume theory. This theory has a variety of interesting symmetries some of which are obscure in the Lagrangian formulation of the theory. However, as summarized in this review, an alternative approach is to construct all of its on-shell tree-level scattering

A new series of correlation inequalities for random field spin systems is proven rigorously. First one corresponds to the well-known Schwartz–Soffer inequality. These are expected to rule out incorrect results calculated in effective theories and numerical studies. The large N expansion with the replica method for random field systems as an example is checked by these inequalities. It is shown that

Q -systems provide an efficient way of solving Bethe equations. We formulate here Q -systems for both the isotropic and anisotropic open Heisenberg quantum spin-1/2 chains with diagonal boundary magnetic fields. We check these Q -systems using novel discrete Wronskian-type formulas (relating the fundamental Q -function and its dual) that involve the boundary parameters.

We discuss solvable multistate Landau–Zener (MLZ) models whose Hamiltonians have commuting partner operators with ∼1/ τ -time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ

In this review we discuss recent advances in the computation of one-point functions in defect conformal field theories with holographic duals. We briefly review the appearance of integrable spin chains in ##IMG## [http://ej.iop.org/images/1751-8121/53/28/283001/aab15fbieqn001.gif] super Yang–Mills theory and reformulate the problem of computing one-point functions to determining overlaps between Bethe

This is a write-up of the lectures given in Young Researchers Integrability School 2017. The main goal is to explain the connection between the ODE/IM correspondence and the classical integrability of strings in AdS. As a warm up, we first discuss the classical three-point function of the Liouville theory. Our starting point is the well-known fact that the classical solutions to the Liouville equation

We give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar ##IMG## [http://ej.iop.org/images/1751-8121/53/28/283004/aab7137ieqn001.gif] super Yang–Mills theory (and of the dual string model) in terms of a solution of a Riemann–Hilbert problem for a finite set of functions. We review the underlying QQ relations

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This is the writeup of the lectures given at the Winter School ‘YRISW 2018’ to appear in a special issue of J. Phys. A: Math. Theor. In the first part of these lecture notes we review some important facts about 4D ##IMG## [http://ej.iop.org/images/1751-8121/53/28/283005/aab7f66ieqn5.gif] {$\mathcal{N}=2$} SCFTs. We begin with basic textbook material, the supersymmetry algebra and its massless representations

These notes provide an introduction toward Wilson loops in ##IMG## [http://ej.iop.org/images/1751-8121/53/28/283003/aab2477ieqn001.gif] supersymmetric Yang–Mills theory with a focus toward their integrability properties. In addition to a brief discussion of exact results for the circular Wilson loop and the cusp anomalous dimension, the notes focus on non-local symmetries, utilizing the integrability

We construct an ϵ -deformation of W algebras, corresponding to the additive version of quiver ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275401/aab9275ieqn6.gif] {${\text{W}}_{q,{t}^{-1}}$} algebras which feature prominently in the 5D version of the BPS/CFT correspondence and refined topological strings on toric Calabi–Yau’s. This new type of algebras fill in the missing intermediate level between

The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced

We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage time probability density function for different values of the index of stability and the skewness parameter. A comparison with results using the Langevin approach to

The quantum metric tensor G ij for parameterised families of quantum states, in particular the trace G = tr G ij , depends on the symmetry of the system (e.g. time-reversal), and the dimension N of the underlying matrices. Modelling the families by the stationary Gaussian ensembles of random-matrix, theory, we calculate the probability distribution of G , exactly for N = 2, and approximately for N

The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However

Trace formulas play a central role in the study of spectral geometry and in particular of quantum graphs. The basis of our work is the result by Kurasov which links the Euler characteristic χ of metric graphs to the spectrum of their standard Laplacian. These ideas were shown to be applicable even in an experimental context where only a finite number of eigenvalues from a physical realization of quantum

We present a derivation of the Feynman–Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. As found previously, this generating function is given by a Feynman–Vernon-like influence functional, with only time shifts in the kernels coupling the forward and

We construct and study the 6D dual superconformal algebra. Our construction is inspired by the dual superconformal symmetry of massless 4D ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn2.gif] {$\mathcal{N}=4$} SYM and extends the previous construction of the enhanced dual conformal algebra for 6D ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275402/aab8ff6ieqn3.gif] {$\mathcal{N}=\left(1