Trace Class and Statistical Operators

Maurice A. de Gosson

Shuhui Gao, Yuan Li, Nana Wei

Maria Alberta Alberti, Paolo Cotta-Ramusino, G. Ramella

The Liouville−von Neumann equation and a useful decomposition of the resolvent of the generator of the time evolution operators are obtained in the formulation of quantum statistics by means of the pair of Banach spaces (τc, B), where τc is the space of the ’’trace−class’’ operators and B is the space of all bounded operators, defined on a Hilbert space.

V. I. Yukalov, E. P. Yukalova

A measure of correlations for statistical systems is advanced, called correlation index. The measure is general, being applicable to quantum and classical, equilibrium and nonequilibrium statistical systems. After formulating the general notion of correlation indices for arbitrary trace-class operators, the calculation of the correlation indices are illustrated by several examples of density operators and reduced density matrices. The computation of the correlation indices for equilibrium systems is exemplified for bosonic systems with the Bose-Einstein condensate, superconducting systems, and for spin systems. Correlation indices for nonequilibrium systems are considered for nonlinear dynamics of spin and pseudospin systems.

冬彦 田中

Let us consider functions from a locally compact metric space to trace- class operators on a separable Hilbert space.It is a basic framework in constructing quantum statistical models.In theoretical development, Holevo gave one definition of continuity of those functions in a more general setting.A regularity condition of quantum statistical models is derived from this definition but it seems complicated.We show that it is rewritten in a simple form.