Abstract:
A rigorous mathematical description is given of equilibrium states of quantum systems
on the basis of the theory of the canonical ensemble. For the $m$-particle density matrices
of the canonical ensemble in finite volume relations are obtained which go over into the
Kirkwood–Salzburg integral equations in the case of infinite Systems. Existence and
uniqueness is proved for the limit $m$-particle density matrices of the canonical ensemble;
their analytic dependence on the density is investigated; and it is shown that the canonical
and the grand canonical ensemble are equivalent in the thermodynamic limit.
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