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

It is proved that the q uantization of the Volkovyski endash Sinai model of ideal gas (in the Maxwell endash Boltzmann statistics) enjoys at the thermodynamical limit the property of quantum mixing in the following sense: lim|t|→∞limm/L→ρm,L→∞ωβ ,Lm(eiHmt/ℎxAe-iHmt/mCB)=limm/L→ρm,L→∞ωβ,Lm( A)·limm/L→ρm,L→∞ωβ,Lm(B ). Here Hm is the Schroedinger 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; ωmβ,L(A) is the corresponding quantum Gibbs state. Moreover, one has limm/L→ρm,L→∞ωβ,m(A)=Pρ,β(a), where Pρ,β(a) is the classical Gibbs measure. The consequent notion of quantum ergodicity is also independently proven. copyright 1996 American Institute of Physics