Statistical Ensemble of Canonical Modes

H. A. Buchdahl

Diego R. Alcoba, Roberto C. Bochicchio, G. E. Massacessi +2 more

We deal with many-electron systems having a noninteger number of electrons, which cannot be described properly by means of pure states or by canonical statistical ensemble states. The study of the one-electron reduced density matrix for these systems raises the problem of its representability in statistical ensembles of grand canonical type. We derive the necessary and sufficient conditions for the representability of the one-electron reduced density matrix of grand-canonical statistical ensembles.

Gregor Skačej, P. Ziherl

Walter Hahn, Boris V. Fine

We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable. In the context of the foundations of quantum statistical physics, this result justifies the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles.

Stephen L. Adler, Lawrence Paul Horwitz

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.