Ergodic properties of the quantum ideal gas in the Maxwell-Boltzmann statistics

It is proved that the quantization of the Volkovyski-Sinai model of ideal gas (in the Maxwell-Boltzmann statistics) enjoys at the thermodynamical limit the property of quantum mixing in the following sense: lim(\t\-->infinity) lim(m,L-->infinity) lim(m,L-->infinity/m/L-->rho) omega(beta,L)(m) (e(iHmt/h) x Ae(-iHmt/h) B) = lim(m,L-->infinity/m/L-->rho) omega(beta,L)(m) (A). lim(m,L-->infinity/m/L-->rho) omega(beta,L)(m) (B). Here Hm is the Schrodinger operator of m free particles moving on a circle of length L:A and B are the Weyl quantization of two classical observables a and b; omega(beta,L)(m) (A) is the corresponding quantum Gibbs state. Moreover, one has lim(m,L-->infinity/m/L-->rho) omega(beta,m) (A) = P-rho,P-beta(alpha), where P-rho,P-beta(alpha) is the classical Gibbs measure. The consequent notion of quantum ergodicity is also independently proven. (C) 1996 American Institute of Physics.