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Steady states of harmonic oscillator chains and shortcomings of harmonic heat baths

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  • Tegmark, Max
  • Yeh, Leehwa

Abstract

We study properties of steady states (states with time-independent operators) of systems of coupled harmonic oscillators. Formulas are derived showing how an adiabatic change of the Hamiltonian transforms one steady state into another. It is shown that for infinite systems, sudden change of the Hamiltonian also tends to produce steady states, after a transition period of oscillations. These naturally arising steady states are compared to the maximum-entropy state (the thermal state) and are seen not to coincide in general. The approach to equilibrium of subsystems consisting of n coupled harmonic oscillators has been widely studied, but only in the simple case where n=1. The power of our results is that they can be applied tomore complex subsystems, where n > 1. It is shown that the use of coupled harmonic oscillators as heat baths models is fraught with some problems that do not appear in the simple n=1 case. Specifically, the thermal states that are thought to be achievable through hard-sphere collisions with heat-bath particles can generally not be achieved with harmonic coupling to the heat-bath particles, except approximately when the coupling is weak.

Suggested Citation

  • Tegmark, Max & Yeh, Leehwa, 1994. "Steady states of harmonic oscillator chains and shortcomings of harmonic heat baths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 342-362.
    • Handle: RePEc:eee:phsmap:v:202:y:1994:i:1:p:342-362
    DOI: 10.1016/0378-4371(94)90181-3
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    1. Micheline Thomine-Desmazures, 1965. "L'investigation psychosociologique en milieu rural," Économie rurale, Programme National Persée, vol. 64(1), pages 19-24.
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