Thermodynamics of quantum dissipative many-body systems

TL;DR

This paper develops approximate formulas for thermodynamic properties of quantum many-body systems with dissipation, using a self-consistent harmonic approximation within the Caldeira-Leggett framework, and explores dissipation effects on a quantum phi4-chain.

Contribution

It introduces a variational scheme based on PQSCHA for analyzing dissipative quantum many-body systems, extending classical-like thermodynamic formulas to include quantum and dissipative effects.

Findings

Dissipation significantly influences quantum thermodynamics depending on its parameters.

The PQSCHA provides manageable expressions for quantum thermal averages in dissipative systems.

Application to a quantum phi4-chain reveals nontrivial dissipation effects.

Abstract

We consider quantum nonlinear many-body 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 for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permits to get manageable PQSCHA expressions for quantum thermal averages with a classical Boltzmann factor involving an effective potential and an inner Gaussian average that describes the fluctuations originating from the interplay of quanticity and dissipation. The application of the PQSCHA to a quantum phi4-chain with Drude-like dissipation shows nontrivial effects of dissipation, depending upon its strength and bandwidth.