Monday, January 30, 2012

1201.0578 (S. B. Rutkevich)

Partial thermalization in the quantum chain of harmonic oscillators    [PDF]

S. B. Rutkevich
This preprint contains the English translation of the paper "Relaxation
dynamics of a quantum chain of harmonic oscillators", which was published by
the author in 1980 in the Ukrainian Physical Journal. Comments describing its
motivations, background ideas and results are presented as well. This paper
addressed to the problem of approach to the thermal equilibrium in an isolated
macroscopic quantum system, which was studied on the example of the quantum
chain of weakly interacting harmonic oscillators. In the initial state,
macroscopic energy was supplied to one oscillator (atom) in the chain.
Subsequent evolution of the quantum state of the whole chain was determined due
to the model integrability. The main subject of interest was the time evolution
of the reduced density operators characterizing the quantum state of a
particular atom. On the short time-scale, the energy perturbation expands along
the chain with the velocity of the fastest phonon mode. On the long-time scale,
the single-atom density operators display strong fluctuations around the
canonical Gibbs distribution. These fluctuations are caused by the degeneracy
of the energy level differences (presence of resonances) in the model of
coupled harmonic oscillators. After lifting this degeneracy, fluctuations are
suppressed providing, that the reduced density operator of each atom in the
chain becomes very close to the Gibbs distribution at almost any time moment.
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