Abstract
A linear, harmonic, isotopically impure crystal is placed into contact with two harmonic oscillator heat baths, each at a different temperature. Force fluctuations on the ends of the crystal are studied in the nonequilibrium steady state that results from the ultimate evolution of the coupled crystal-heat baths. The exact behavior of steady state force fluctuations is obtained in general and examined in detail for periodic or randomly disordered isotopic lattices. Numerical results for the periodic crystal reveal unexpected complexity in the temporal decay of the force autocorrelation function. From exact expressions for the entire force distribution functions we show that, in general, the distribution is Gaussian and non-Markovian. However, on a coarse grained, semimicroscopic time scale (∼10−12 sec), the Gaussian force distribution is purely random and in accord with the usual assumptions about heat baths. One case of a macroscopic decay time occurs when one bath is initially at T =0°K in contact with a randomly disordered lattice.
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