Thermodynamics of dissipative quantum systems by effective potential

TL;DR

This paper develops classical-like formulas using an effective potential to evaluate thermal averages in dissipative quantum systems, incorporating quantum fluctuations, and demonstrates the method with a double-well potential example.

Contribution

It introduces a pure-quantum self-consistent harmonic approximation framework for dissipative quantum systems, providing explicit formulas involving an effective potential and Gaussian averages.

Findings

Derived formulas for thermal averages with dissipation

Applied method to double-well potential with Ohmic dissipation

Showed quantum fluctuations influence on coordinate distribution

Abstract

Classical-like formulas are given in order to evaluate thermal averages of observables belonging to a quantum nonlinear system with dissipation described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys. (N.Y.) 149, 374 (1983)]. The underlying scheme is the pure-quantum self-consistent harmonic approximation, which leads to expressions with a Boltzmann factor involving an effective potential and with a Gaussian average. The latter describes the effect of the fluctuations of purely quantum origin. As an illustration we calculate the coordinate probability distribution for a double-well potential in the presence of various degrees of Ohmic dissipation.