Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand canonical Ensembles
arXiv:cond-mat/0306306 · doi:10.1016/j.physa.2003.10.072
Abstract
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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