Effective potential for dissipative quantum systems

TL;DR

This paper develops approximate classical-like formulas to evaluate thermal averages in dissipative quantum systems modeled by the Caldeira-Leggett framework, covering linear, nonlinear dissipation, and many degrees of freedom.

Contribution

It introduces a unified approach to approximate thermal averages in dissipative quantum systems with various dissipation types and multiple degrees of freedom.

Findings

Derived classical-like formulas for thermal averages

Extended framework to nonlinear dissipation

Applicable to systems with many degrees of freedom

Abstract

We consider quantum nonlinear systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas are derived in order to evaluate thermal averages of observables: the cases of linear and nonlinear dissipation are considered, and the framework is extended to the case of many degrees of freedom.