Related papers: Bilateral Birth and death process in quantum calcu…
A new model maps a quantum random walk described by a Hadamard operator to a particular case of a birth and death process. The model is represented by a 2D Markov chain with a stochastic matrix, i.e., all the transition rates are positive,…
Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
Modeling and reasoning about concurrent quantum systems is very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and…
We introduce and study a fractional variant of the linear birth-death process, namely, the generalized fractional linear birth-death process (GFLBDP) which is defined by taking the regularized Hilfer-Prabhakar derivative in the system of…
A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT…
Duality relations between continuous-state and discrete-state stochastic processes with continuous-time have already been studied and used in various research fields. We propose extended duality relations, which enable us to derive…
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the…
This work extends our previous studies of two-photon annihilation into baryon-antibaryon pairs from spin-1/2 octet to spin-3/2 decuplet baryons. Our approach is based on perturbative QCD and treats baryons as quark-diquark systems. Using…
We study the dynamics of quantum systems interacting with a stream of entangled qubits. Under fairly general conditions, we present a detailed framework describing the conditional dynamical maps for the system, called quantum trajectories,…
In this paper we study strong solutions of some non-local difference-differential equations linked to a class of birth-death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of…
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional…
The quantum dynamics of a two-state system (qubit) can be governed by means of external control parameters present in time-dependent bias pulses of special forms. We consider the class of biases for which the time evolution equation without…
The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…
A novel approach is employed and developed to derive transition probabilities for a simple time-inhomogeneous birth-death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases.…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
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…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…