Dissipative Quantum Systems and the Heat Capacity Enigma

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.

13 pages

References in corpus (5)

• Finite quantum dissipation: the challenge of obtaining specific heat
• Specific heat anomalies of open quantum systems
• Low temperature Thermodynamics in the Context of Dissipative Diamagnetism
• Landau-Drude Diamagnetism: Fluctuation, Dissipation and Decoherence
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• Partition of kinetic energy and magnetic moment in dissipative diamagnetism
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• Quantum Dynamics of a Dissipative and Confined Cyclotron Motion
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• Stochastic thermodynamics and the Ericsson nano engine -- Efficiency from equilibrium results
• Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field
• Quantum Counterpart of Equipartition Theorem in Quadratic Systems
• Free energy of a charged oscillator in a magnetic field and coupled to a heat bath through the momentum variables
• Classical and quantum Brownian motion in an electromagnetic field
• Weak-coupling limits of the quantum Langevin equation for an oscillator
• Quantum Counterpart of Equipartition Theorem: A Möbius Inversion Approach