Classical and quantum Brownian motion in an electromagnetic field

TL;DR

This paper investigates the classical and quantum dynamics of a Brownian particle in electromagnetic fields, revealing how its probability distribution evolves through classical motion, rotation, and spreading, using Langevin and path-integral methods.

Contribution

It provides a comparative analysis of classical and quantum Brownian motion in electromagnetic fields using Langevin and path-integral frameworks.

Findings

Classical motion of the particle's center of mass is characterized.

Quantum probability distribution exhibits rotation and spreading.

The evolution can be described as a superposition of classical and quantum effects.

Abstract

The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and Caldeira-Leggett framework for the quantum problem. We study the time evolution in configuration space of the probability distribution of an initial pure state represented by an asymmetrical Gaussian wave function and show that it can be described as the superposition of (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c) a spreading processes along the principal axes.