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arXiv:1205.2068 · Physical Review E

Equilibration and thermalization of the dissipative quantum harmonic oscillator in a nonthermal environment

D. Pagel, Andreas Alvermann, Holger Fehske

Published Jan 22, 2013• 17 citations
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Abstract

We study the dissipative quantum harmonic oscillator with general nonthermal preparations of the harmonic oscillator bath. The focus is on equilibration of the oscillator in the long-time limit and the additional requirements for thermalization. Our study is based on the exact solution of the microscopic model obtained by means of operator equations of motion, which provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We find a hierarchy of conditions for thermalization, together with the relation of the asymptotic temperature to the energy distribution in the initial bath state. We discuss the presence and absence of equilibration for the example of an inhomogeneous chain of harmonic oscillators, and we illustrate the general findings about thermalization for the nonthermal environment that results from a quench.

DOI
10.1103/physreve.87.012127

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