Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian

Details Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian

2003-11-12

arxiv.org/abs/cond-mat/0311288v1

Annual of Physics 313, 1 (2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.aop.2004.04.007

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.

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