Quantum Brownian Motion

Abstract

A tutorial discussion is given of path integral methods for dealing with the fluctuations of a quantum variable (“particle”) coupled to a large quantum system (“environment”) that provides a friction force linearly proportional to the particle velocity. It is shown explicitly how the sum over paths can be reduced to an ordinary double integral for the time evolution of the density matrix describing the particle when the potential in which it moves has one of the following three simple forms: constant, linear, or quadratic. A brief summary is given of results that can be obtained by this method.