Related papers: Birth and death processes and quantum spin chains
There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…
In this paper one presents the extension of the transient analysis of the class of continuous-time birth and death processes defined on non-negative integers with special transitions from and to the origin. From the origin transitions can…
In this paper, we consider an extended coined Szegedy model and discuss the existence of the point spectrum of induced quantum walks in terms of recurrence properties of the underlying birth and death process. We obtain that if the…
We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but…
The aim of this paper is to study some models of quasi-birth-and-death (QBD) processes arising from the theory of bivariate orthogonal polynomials. First we will see how to perform the spectral analysis in the general setting as well as to…
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain…
The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…
The dynamical behaviour of the quantum state of different quantum spin chains, with designed site dependent interaction strengths, is analyzed when the initial state belongs to the one excitation subspace. It is shown that the inhomogeneous…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show…
Lattice birth-and-death Markov dynamics of particle systems with spins from the set of non-negative integers are constructed as unique solutions to certain stochastic equations. Pathwise uniqueness, strong existence, Markov property and…
A symmetric relation in the probabilistic Green's function for birth-death chains is explored. Two proofs are given, each of which makes use of the known symmetry of the Green's functions in other contexts. The first uses as primary tool…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions…
We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor…
Motzkin chain is a model of nearest-neighbor interacting quantum $s=1$ spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic…
In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair…
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
The recently found hypergeometric multiple orthogonal polynomials on the step-line by Lima and Loureiro are shown to be random walk polynomials. It is proven that the corresponding Jacobi matrix and its transpose, which are nonnegative…