Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand canonical Ensembles

Details Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand canonical Ensembles Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand canonical Ensembles

2003-06-11

arxiv.org/abs/cond-mat/0306306v2

Physics

Condensed Matter

Statistical Mechanics

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Scientific paper

10.1016/j.physa.2003.10.072

Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain the analogous Bloch equation and the corresponding hierarchy reduced equations for the identical interacting many-body system. We discuss their possible solutions and applications.

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