Equivalence of Gibbs ensembles for quantum systems obeying Maxwell-Boltzmann statistics

A generating functional of the canonical ensemble is introduced for quantum systems of particles obeying Maxwell-Boltzmann statistics. Power estimates for the quantum analogs of the particle distribution functions of the canonical and grand canonical ensembles are obtained for systems of particles with hard cores. It is shown on the basis of the power estimates that limiting generating functionals exist for the systems under consideration and satisfy the same Bogolyubov equation. The ensembles are equivalent in this sense.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–8, July, 1984.The authors thank É. A. Arinshtein for useful discussion.