D. Pagel, A. Alvermann, H. Fehske
We study the dissipative quantum harmonic oscillator with general non-thermal preparations of the harmonic oscillator bath. The focus is on the 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. The solution provides us with the time evolution of the central oscillator density matrix in terms of the propagating function. We prove equilibration of the central oscillator under weak assumptions and 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 illustrate the general findings for the example of an infinite chain of harmonic oscillators, where a non-thermal environment is obtained under natural assumptions.
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http://arxiv.org/abs/1205.2068
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