Related papers: Quantum Dynamics in Stochastic Mechanics
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum Mechanics in presence of non-interacting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary…
We examine the dynamics of statistical fluctuations in nuclear matter. Linear response functions for the average phase space density are derived within Landau theory. Properties of the stochastic forces are deduced from the quantal…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles…
We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and…
We discuss the random motion of charged test particles driven by quantum electromagnetic fluctuations at finite temperature in both the unbounded flat space and flat spacetime with a reflecting boundary and calculate the mean squared…
This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
We treat a relativistically moving particle interacting with a quantum field from an open system viewpoint of quantum field theory by the method of influence functionals or closed-time-path coarse-grained effective actions. The particle…
We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on…
So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this paper, we present a stochastic model with time-correlated noise that…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
Brownian oscillator, i.e. a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the…
In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by H\"older continuous functions of order $H>\frac12$. As an application, we consider stochastic differential…
We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…