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The harmonic oscillator in a heat bath

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Abstract

We study the time evolution of a quantum-mechanical harmonic oscillator in interaction with an infinite heat bath, which is supposed to be initially in the canonical equilibrium at some temperature. We show that the oscillator relaxes from an arbitrary initial state to its canonical state at the same temperature, and that in the weak coupling limit the relaxation is Markovian, that is exponential. In contrast to earlier treatments of the problem [4, 5], the results are obtained without assuming any particular special form for the self-interaction of the heat bath. No use is made of coarse graining, finite memory assumptions or randomly varying Hamiltonians.

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  1. Mathematical Institute, Oxford, U K

    E. B. Davies

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  1. E. B. Davies
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Davies, E.B. The harmonic oscillator in a heat bath. Commun.Math. Phys. 33, 171–186 (1973). https://doi.org/10.1007/BF01667915

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  • DOI: https://doi.org/10.1007/BF01667915

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