FROM QUANTUM DYNAMICS TO THE CANONICAL DISTRIBUTION - GENERAL PICTUREAND A RIGOROUS EXAMPLE

Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and assume that the whale system is initially in a pure state (which can be far from e quilibrium) with small energy fluctuation. Under the ''hypothesis of e qual weights for eigenstates,'' we derive the canonical distribution i n the sense that, at sufficiently large and typical time, the (instant aneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation ca n be rigorously established without any unproven hypotheses.