Statistical Mechanics of Assemblies of Coupled Oscillators

It is shown that a system of coupled harmonic oscillators can be made a model of a heat bath. Thus a particle coupled harmonically to the bath and by an arbitrary force to a fixed center will (in an appropriate limit) exhibit Brownian motion. Both classical and quantum mechanical treatments are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70752/2/JMAPAQ-6-4-504-1.pd