Quasiclassical Equations of Motion for Nonlinear Brownian Systems

TL;DR

This paper derives phenomenological equations of motion for nonlinear Brownian systems using a path-integral approach, comparing quantum and classical results, especially for systems interacting with harmonic oscillator baths.

Contribution

It introduces a formalism connecting quantum decoherence with classical equations of motion for nonlinear Brownian systems, including exact solutions for linear interactions.

Findings

Exact equations for linear interactions derived.

Quantum and classical perturbation results compared.

Framework applicable to systems with harmonic oscillator baths.

Abstract

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.