Related papers: Universal and nonuniversal probability laws in Mar…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
We consider the discrete time unitary dynamics given by a quantum walk on the lattice $\Z^d$ performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to…
We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes…
Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [B. Vacchini, Phys. Rev. Lett. 117, 230401 (2016)]. These dynamics have been defined in…
The dynamics of open quantum systems is often solved by stochastic unravellings where the average over the state vector realizations reproduces the density matrix evolution. We focus on quantum jump descriptions based on the rate operator…
The dynamics of open quantum systems is often modelled using master equations, which describe the expected outcome of an experiment (i.e., the average over many realizations of the same dynamics). Quantum trajectories, instead, model the…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
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…
In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…
Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincar\'e (A) 70, 429…
With many Hamiltonians one can naturally associate a |Psi|^2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field…
Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time…