Relativistic and non-relativistic quantum Brownian motion in an anisotropic dissipative medium

TL;DR

This paper develops a comprehensive quantum Langevin framework to analyze relativistic and non-relativistic quantum Brownian motion in anisotropic dissipative media, providing explicit solutions and applications.

Contribution

It introduces a unified approach to quantum Brownian motion in anisotropic media, deriving general equations and explicit solutions for both relativistic and non-relativistic cases.

Findings

Derived a general quantum Langevin equation for anisotropic media

Obtained explicit solutions for equations of motion

Provided examples demonstrating applicability

Abstract

Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum Langevin equation is derived and explicit expressions for quantum-noise and dynamical variables of the system are obtained. The equations of motion for the canonical variables are solved explicitly and an expression for the radiation-reaction of a charged particle in the presence of a dissipative-medium is obtained. Some examples are given to elucidate the applicability of this approach.