Related papers: Quantum vs Classical Birth and Death Processes; Ex…
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…
A coinless quantisation procedure of general reversible Markov chains on graphs is presented. A quantum Hamiltonian H is obtained by a similarity transformation of the fundamental transition probability matrix K in terms of the square root…
We present 15 explicit examples of discrete time Birth and Death processes which are exactly solvable. They are related to the hypergeometric orthogonal polynomials of Askey scheme having discrete orthogonality measures. Namely, they are…
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with…
We study a class of quantum Markov processes that, on the one hand, is inspired by the micromaser experiment in quantum optics and, on the other hand, by classical birth and death processes. We prove some general geometric properties and…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of…
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 study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
We consider a stochastic spatial point process with births and deaths on $\mathbb{R}^d$, with the hard-core property that at any time the balls of radius half of any two points do not overlap. We give explicit construction of the process.…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
The classical trajectories of a particle governed by the PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in depth. It is known that almost all trajectories that begin at a classical turning point…
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…