Dissipative Quantum Systems and the Heat Capacity Enigma

TL;DR

This paper investigates how dissipation affects the heat capacity of a quantum charged particle in a magnetic field, comparing two theoretical approaches and revealing surprising parameter dependencies and boundary effects.

Contribution

It provides exact analyses of the specific heat in dissipative quantum systems using two different statistical mechanics approaches, highlighting differences and boundary influences.

Findings

Low-temperature specific heat follows power-law dependence consistent with the third law.

High-temperature specific heat aligns with classical equipartition.

Distinct parameter dependencies and boundary effects are observed between the two approaches.

Abstract

We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behavior of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature-dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary-confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit (time going to infinity) is taken, seems to assume significance.