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 properties of mixing and ergodicity with respect to the quantum canonical Gibbs state. Plus, the average over the quantum state of a pseudo-differential operator is exactly the average over the classical canonical measure of its Weyl symbol.