arXiv:0911.1584 · Physical Review E

Dissipative quantum systems and the heat capacity

Sushanta Dattagupta, Jishad Kumar, Subhasis Sinha, P. A. Sreeram

Published Mar 31, 2010• 28 citations

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 behaviors 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 (t-->infinity) is taken seems to assume significance.

DOI: 10.1103/physreve.81.031136

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arXiv:0911.1584 · Physical Review E

Dissipative quantum systems and the heat capacity

Sushanta Dattagupta, Jishad Kumar, Subhasis Sinha, P. A. Sreeram

Published Mar 31, 2010• 28 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.81.031136

Related papers

Quantum Brownian motion and the Third Law of thermodynamics

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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsSep 5, 2002163 citations

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Malay Bandyopadhyay, Sushanta Dattagupta

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{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

denote the average kinetic and potential energies of individual thermostat oscillators. The net averaging is twofold; the first one is over the Gibbs canonical state for the thermostat, giving

{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

, and the second one, denoted by $\ensuremath{\langle}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\rangle}$, is over the frequencies $\ensuremath{\omega}$ of the bath oscillators which contribute to

{E}_{k}

and

{E}_{p}

according to probability distributions ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$, respectively. The relationship of the present quantum version of the equipartition theorem with that of the fluctuation-dissipation theorem (within the linear-response theory framework) is also explored. Further, we investigate the influence of the external magnetic field and the effect of different dissipation processes through Gaussian decay and Drude and radiation bath spectral density functions on the typical properties of ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$. Finally, the role of system-bath coupling strength and the memory effect is analyzed in the context of average kinetic and potential energies of the dissipative charged magneto-oscillator.