Related papers: On the compatibility between the Markov property a…
This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous- and discrete-time cases. The sufficient conditions for the existence and uniqueness of a…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the…
A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a…
We propose a model of time evolution of quantum objects which unites the unitary evolution and the measurement procedures. The model allows to treat the time on equal footing with other dynamical variables.
A central challenge in quantum physics is to understand the structural properties of many-body systems, both in equilibrium and out of equilibrium. For classical systems, we have a unified perspective which connects structural properties of…
In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…
We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing…
A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving…
Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
For a continuous-time Markov process, we characterize the law of the first jump location when started from an arbitrary initial distribution, in terms of the invariant distribution of an auxiliary Markov process. This could be of interest…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
We study the dynamics of a driven non-Hermitian superconducting qubit which is perturbed by quantum jumps between energy levels, a purely quantum effect with no classical correspondence. The quantum jumps mix the qubit states leading to…
Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding…
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is…
We construct a class of quantum stochastic models of reservoir driven many-particle systems that are the natural counterparts of certain extensively studied classical ones, which have been shown to exhibit good hydrodynamical behaviour. Our…
We consider a stationary Markovian evolution with values on a disjointly partitioned set space $I\sqcup {\cal E}$. The evolution is visible (in the sense of knowing the transition probabilities) on the states in $I$ but not for the states…
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…