Related papers: Classical Markovian Kinetic Equations: Explicit Fo…

We investigate the role of coherence and Markovianity in finding an answer to the question whether the outcomes of a projectively measured quantum stochastic process are compatible with a classical stochastic process. For this purpose we…

We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…

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…

We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of…

Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…

Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…

A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the…

We derive sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide a natural parameterizations of the dynamical map being a…

This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial…

A system of spins coupled to a bath is a traditional setup in open quantum systems. Through Heisenberg's equation, the spin dynamics can be modeled by a set of first-order differential equations. Interpreting the terms as colored noise and…

It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…

We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…

A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly…

Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between…

The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these…

The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…

I describe, in the simplified context of finite groups and their representations, a mathematical model for a physical system that contains both its quantum and classical aspects. The physically observable system is associated with the space…

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such…