Abstract:
A quantum chain of $N$ harmonic oscillators is considered using perturbation theory methods. The author derives the density matrix dynamics of a subsystem containing $N'$ oscillators when the whole chain relaxes from some initial pure state. The Gibbs distribution is shown to be the time-average thermodynamical limit of the relevant statistical operator. The presence of a weak anharmonic interaction in the system makes the density matrix deviations from the canonical distribution extremely rare.
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