Second quantized reduced Bloch equations and the exact solutions for pairing Hamiltonian |
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Authors: | Liqiang Wei Chiachung Sun |
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Institution: | a Institute for Theoretical Atomic, Molecular and Optical Physics, Harvard University, Cambridge, MA 02138, USA b Institute of Theoretical Chemistry, Jilin University Changchun, Jilin 130023, PR China c Institute of Biophysics, Chinese Academy of Science, Beijing 100101, PR China |
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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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Keywords: | 05 30-d 71 10 -w 71 10 Fd 71 10 Li |
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