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

Liqiang Wei·C. C. Sun
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Abstract

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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Liqiang Wei, C. C. Sun. 2003-11-12. Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian. https://doi.org/10.1016/j.aop.2004.04.007

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