### Max Tegmark's quantum library: steady

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## STEADY STATES OF HARMONIC OSCILLATOR CHAINS AND SHORTCOMINGS OF HARMONIC
HEAT BATHS

### Authors:

Max Tegmark & Leehwa Yeh

### Abstract:

We study properties of steady states (states with time-independent density
operators) of systems of coupled harmonic oscillators. Formulas are derived
showing how 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 to
more complex subsustems, 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 though to be achievable through hard-sphere collisions with heat-bath
particles can generally {\it not} be achieved with harmonic coupling to
the heat-bath particles, except approximately when the coupling is weak.

### Reference info:

Published in Physica A, **202**, 342-362 (1994)

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This page was last modified July 1, 1998.
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