We derive a continuity equation to study transport properties in a ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445308/aabb513ieqn2.gif] {$\mathcal{P}\mathcal{T}$} -symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a transport coefficient to characterize the efficiency of transport of each state

Given two orthonormal bases ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445304/aabad78ieqn1.gif] {$\mathcal{A}$} and ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445304/aabad78ieqn2.gif] {$\mathcal{B}$} , the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring ##IMG## [http://ej.iop.org/images/1751-812

We study a diffusion process on a finite interval under the influence of a controllable drift where the particle resets to the left-hand side upon reaching the right-hand side. Assigning a pay-off for being nearer the right-hand side, but a penalty for reaching it, induces an inherent trade-off. We seek the drift feedback that maximises the long-term reward. By reducing the problem to a constrained

Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete time quantum walk irrespective of the initial state using two different approaches. First, we present and analyze a deterministic sequence of coin operators which

We introduce a new quantum optimization algorithm for dense linear programming problems, which can be seen as the quantization of the interior point predictor–corrector algorithm [1] using a quantum linear system algorithm [2]. The (worst case) work complexity of our method is, up to polylogarithmic factors, ##IMG## [http://ej.iop.org/images/1751-8121/53/44/445305/aabb439ieqn1.gif] {$O\left(L\sqrt

A study is presented of superintegrable quantum systems in two-dimensional Euclidean space E 2 allowing the separation of variables in Cartesian coordinates. In addition to the Hamiltonian H and the second order integral of motion X , responsible for the separation of variables, they allow a third integral that is a polynomial of order N ( N ⩾ 3) in the components p 1 , p 2 of the linear momentum.

The Bethe ansatz solution of periodic TASEP is formulated in terms of a ramified covering from a Riemann surface to the sphere. The joint probability distribution of height fluctuations at n distinct times has in particular a relatively simple expression as a function of n variables on the Riemann surface built from exponentials of Abelian integrals, traced over the ramified covering and integrated

Stochastic logistic and θ -logistic models have many applications in biological and physical contexts, and investigating their structure is of great relevance. In the present paper we provide the closed form of the path-like solutions for the logistic and θ -logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their moments. We

Superstatistics describes nonequilibrium steady states as superpositions of canonical ensembles with a probability distribution of temperatures. Rather than assume a certain distribution of temperature, recently [2020 J. Phys. A: Math. Theor. 53 045004] we have discussed general conditions under which a system in contact with a finite environment can be described by superstatistics together with a

We introduce an analytical method to generate the pathway of a closed protein-bound DNA minicircle. We develop an analytical equation to connect two open curves smoothly and use the derived expressions to join the ends of two helical pathways and form models of nucleosome-decorated DNA minicircles. We find that the simplest smooth connector which satisfies the boundary conditions at the end points

Given a non-empty closed convex subset F of density matrices, we formulate conditions that guarantee the existence of an F-morphism (namely, a completely positive trace-preserving linear map that maps F into itself) between two arbitrarily chosen density matrices. While we allow errors in the transition, the corresponding map is required to be an exact F-morphism. Our findings, though purely geometrical

We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying parameters. We derive the underlying Bäcklund transformations, symmetry structure and requirements to satisfy Painlevé property.

Using light-cone gauge formulation, massive arbitrary spin irreducible fields and massless (scalar and spin one-half) fields in three-dimensional flat space are considered. Both the integer spin and half-integer spin fields are studied. For such fields, we provide classification for cubic interactions and obtain explicit expressions for all cubic interaction vertices. We study two forms of the cubic

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S 1 × M 3 with a non-trivial holonomy of a discrete global symmetry along the S 1 . For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern–Simons and Rozansky–Witten

The entanglement witness is an important tool to detect entanglement. In 2017 an idea considering a pair of Hermitian operators in product form was published, which is called ultrafine entanglement witnessing. In 2018 some rigorous results were given. Here we improve their work. First we point this idea can be directly derived from an earlier concept named joint separable numerical range and explain

Finding the classical capacity of a quantum channel is not easy, yet we are able to analytically calculate this capacity for new channels. We analyze the bounds of the Holevo capacity and classical capacity for the generalized Pauli channels. In particular, by generalizing earlier results for the Weyl channels, we obtain the lower and upper bounds of the Holevo capacity and show that, if these bounds

Results are presented for the conservation laws (CLs) for the optical Bloch equations (OBEs) for the Λ scheme under action of two light fields. The method of multipliers (variational derivative method) is used to obtain CLs which are dependent on the density-matrix elements. Results are classified and discussed by the phenomenological parameters and processes characteristic for OBEs, like the relaxation

Wilson’s original formulation of the renormalization group is perturbative in nature. We here present an alternative derivation of the infinitesimal momentum shell renormalization group, akin to the Wegner and Houghton scheme, that is a priori exact. We show that the momentum-dependence of vertices is key to obtain a diagrammatic framework that has the same one-loop structure as the vertex expansion

Spatially dependent birth–death processes can be modelled by kinetic models such as the BBGKY hierarchy. Diffusion in infinite dimensional systems can be modelled with Brownian motion in Hilbert space. In this work Doi field theoretic formalism is utilised to establish dualities between these classes of processes. This enables path integral methods to calculate expectations of duality functions. These

In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton’s equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it generalizes the parametrized Hamilton’s equations to any speed required. (ii) Corrects the parametric action on the occasion that the Hamiltonian is small but finite

Attractor black holes in type II string compactifications on K 3 × T 2 are in correspondence with equivalence classes of binary quadratic forms. The discriminant of the quadratic form governs the black hole entropy, and the count of attractor black holes at a given entropy is given by a class number. Here, we show this tantalizing relationship between attractors and arithmetic can be generalized to

We investigate the question which communication tasks can be accomplished within a given operational theory. The concrete task is to find out which communication matrices have a prepare-and-measure implementation with multiple states and a single measurement from a given theory, without using shared randomness. To set a general framework for this question we develop the ultraweak matrix majorization

We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the solutions is: first, we use the system symmetries to describe the evolution in an operator space whose dimension grows polynomially with the number of atoms. Second

The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schrödinger equations whose potentials are required to be shape invariant. Analytical solutions for the energy bound states are obtained for several magnetic fields. The associated

We study singularity confinement phenomena in examples of delay-differential Painlevé equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means

We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitation spectra, the first-order correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely

We consider chaotic (hyperbolic) dynamical systems which have a generating Markov partition. Then, open dynamical systems are built by making one element of a Markov partition a ‘hole’ through which orbits escape. We compare various estimates of the escape rate which correspond to a physical picture of leaking in the entire phase space. Moreover, we uncover a reason why the escape rate is faster than

We consider a multichannel wire with a disordered region of length L and a reflecting boundary. The reflection of a wave of frequency ω is described by the scattering matrix ##IMG## [http://ej.iop.org/images/1751-8121/53/42/425003/aaba215ieqn2.gif] {$\mathcal{S}\left(\omega \right)$} , encoding the probability amplitudes to be scattered from one channel to another. The Wigner–Smith time delay matrix

In this work, a systematic study, examining the propagation of periodic and solitary waves along the magnetic field in a cold collision-free plasma, is presented. Employing the quasi-neutral approximation and the conservation of momentum flux and energy flux in the frame co-traveling with the wave, the exact analytical solution of the stationary solitary pulse is found analytically in terms of particle

Given an ensemble of qubits, which we are told consists of a mixture of two pure states, one with probability η 0 and one with probability η 1 , we want to find a POVM that will discriminate between the two states by measuring the qubits. We do not know the states, and for any given qubit, we do not know which of the two states it is in. This can be viewed as learning a POVM from quantum data. Once

Most natural complex systems exhibit fluctuations-driven processes, which work at far from equilibrium states, and are generally dissipative processes, for instance living cells. We studied this phenomenon within the stochastic framework by taking a set of nonequilibrium , bimolecular , autocatalytic reactions, originally proposed by Nicolis (1972). We also extended this model to incorporate the concept

We define a supersymmetric quantum mechanics of fermions that take values in a simple Lie algebra ##IMG## [http://ej.iop.org/images/1751-8121/53/42/425401/aabb0c1ieqn3.gif] {$\mathfrak{g}$} . We summarize what is known about the spectrum and eigenspaces of the Laplacian which corresponds to the Koszul differential d . Firstly, we concentrate on the zero eigenvalue eigenspace which coincides with the

We point out that negative specific heat at high energies is a characteristic feature of many ##IMG## [http://ej.iop.org/images/1751-8121/53/42/424001/aab99eeieqn4.gif] {$T\bar{T}$} deformations, both in the original d = 2 case and in d = 1 quantum mechanical cousins. This paper is a contribution to the memorial volume in honor of P G O Freund.

At the onset of an interaction between two initially independent systems, each system tends to experience an increase in its n -Rényi entropies, such as its von Neumann entropy ( n = 1) and its mixedness ( n = 2). We here ask which properties of a system determine how quickly its Rényi entropies increase and, therefore, how sensitive the system is to becoming entangled. We find that the rate at which

We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process with local deterministic bulk dynamics and a stochastic defect that mimicks a random blockage. Exact results are obtained for the compressibility and density correlations for a stationary grandcanonical

We study conformations of the Gaussian polymer chains in d -dimensional space in the presence of an external field with the harmonic potential. We apply a path integral approach to derive an explicit expression for the probability distribution function of the gyration radius. We calculate this function using Monte Carlo simulations and show that our numerical and theoretical results are in a good agreement

We study one-mode Gaussian quantum channels in continuous-variable systems by performing a black-box characterization using complete positivity and trace preserving conditions, and report the existence of two subsets that do not have a functional Gaussian form. Our study covers as a particular limit the case of singular channels, thus connecting our results with their known classification scheme based

The Langmann–Szabo–Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q -ensemble describing U ( N ) Chern–Simons theory

In the theory of extended irreversible thermodynamics (EIT), the flux-dependent entropy function plays a key role; it is a fundamental distinction between EIT and the usual flux-independent entropy function adopted by classical irreversible thermodynamics (CIT). However, its existence, as a prerequisite for EIT, and its statistical origin have never been justified. In this work, by studying the macroscopic

Two constructive proofs on d -majorization and thermo-majorization are provided. In the first part, we present a diagrammatic proof of the equivalence between d -majorization and the existence of a proper stochastic matrix. We explicitly construct the desired stochastic matrix by using a graphical argument. In the second part, we present a constructive proof of the equivalence between the Gibbs-preserving

We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry classification. We find a specific decomposition of the quadratic bosonic Hamiltonian and use it to prove that each quadratic bosonic system is homotopic to a direct

In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to its initial position x 0 at a rate r . The gate switches between an open (absorbing) and closed (reflecting) state according to a two-state Markov chain and can only be detected by the searcher

The analytical properties of the lattice Green function ##IMG## [http://ej.iop.org/images/1751-8121/53/41/415001/aabaa86ueqn4.gif] for the fully anisotropic honeycomb lattice are studied, where ( α 1 , α 2 , α 3 ) are anisotropy parameters with { α j ∈ (0, ∞): j = 1, 2, 3}, and w = u + i v is a complex variable in a ( u , v ) plane. This integral defines a single-valued analytic function G H ( α 1

We present exact soliton solutions of anti-self-dual Yang–Mills equations for G = GL ( N ) on noncommutative Euclidean spaces in four-dimension by using the Darboux transformations. Generated solutions are represented by quasideterminants of Wronski matrices in compact forms. We give special one-soliton solutions for G = GL (2) whose energy density can be real-valued. We find that the soliton solutions

A class of Newtonian forces, determining the acceleration F ( x , y ) of particles in the plane, is F =(Re F ( z ), Im F ( z )), where z is the complex variable x + i y . Curl F is non-zero, so these forces are nonconservative. These complex curl forces correspond to completely integrable Hamiltonians that are anisotropic in the momenta, separable in z and z * but not in x and y if the curl is nonzero

We analyze the Lotka–Volterra n prey-1 predator system without any interspecific interaction between preys, in which each prey species has the relationship of apparent competition with any other prey species. The system we considered in this paper necessarily has a globally asymptotically stable unique equilibrium state. We find the necessary and sufficient condition to determine which equilibrium

In their comment, Angelini et al object to the conclusion of (2019 J. Phys. A: Math. Theor. 52 445002), where we show that in (2013 Phys. Rev. B 87 134201) the exponent ν has been obtained by applying a mathematical relation in a regime where this relation is not valid. We observe that the criticism above on the mathematical validity of such relation has not been addressed in the comment. Our criticism

We study the statistics of the number of records R n for a symmetric, n -step, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P ( R

We investigate non-autonomous solitons in a general coherently coupled nonlinear Schrödinger (CCNLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices

The string corrections of tree-level open-string amplitudes can be described by Selberg integrals satisfying a Knizhnik–Zamolodchikov (KZ) equation. This allows for a recursion of the α ′-expansion of tree-level string corrections in the number of external states using the Drinfeld associator. While the feasibility of this recursion is well-known, we provide a mathematical description in terms of twisted

The known approximation schemes for the solution of the Wetterich exact renormalization group (RG) equation are critically reconsidered, and a new truncation scheme is proposed. In particular, the equations of the derivative expansion up to the ∂ 2 order for a scalar model are derived in a suitable form, clarifying the role of the off-diagonal terms in the matrix of functional derivatives. The natural

We consider point particle that collides with a periodic array of hard-core elastic scatterers where the length of the free flights is unbounded due to infinitely long corridors between the scatterers (the infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT) states that the distribution of the particle displacement divided by ##IMG## [http://ej.iop.org/images/1751-8121/53/41/415004/aabadb6ieqn1

Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum computer. Using the time-dependent variational principle (TDVP)

We applied the thermofield dynamics formalism to analyze how the non-classical properties of the Bell-cat states are influenced by a gradual change of temperature values, in a thermal equilibrium system. To this purpose we calculate the thermal Wigner functions for these states, whose negative volume is associated with non-classical properties, and we evaluate how these non-classical features vary

In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables) in order to work also with the Hopfield model (i.e. a pairwise mean-field neural-network whose couplings are drawn according to Hebb’s learning rule): this is accomplished

We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite W -superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators) graded by a fermionic sector (supersymmetry generators) with anticommutator brackets which are quadratic in the even generators. We analyze the reduction of several

We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single Fredholm determinant representation for the joint distribution function of particle positions with arbitrary initial data. This formula is a generalization of the recent

In the paper Angelini M C et al (2013 Phys. Rev. B 87 134201) we introduced a real-space renormalization group called ensemble renormalization group (ERG) and we applied it to the Edwards–Anderson model, obtaining estimates for the critical exponents in good agreement with those from Monte Carlo simulations. Recently the paper Castellana M (2019 J. Phys. A: Math. Theor. 52 445002) re-examined the ERG

Box-ball system (BBS) is a prominent example of integrable cellular automata in one dimension connected to quantum groups, Bethe ansatz, ultradiscretization, tropical geometry and so forth. In this paper we study the generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and generalized hydrodynamics. The results include the solution to the speed equation for solitons, an intriguing

We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by x and v respectively, we consider two different resetting protocols—(i) complete resetting: here both x and v reset to their initial values x 0 and v 0 at a constant rate r , (ii) partial resetting: here only x resets to x 0 while v evolves without interruption