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Communications in Theoretical Physics

Quantum Statistics for General Quadratic System

Pan Jianwei, Yu Sixia, Zhang Yongde, Siu Gueigu

Published Jan 30, 1999• 0 citations
Publisher

Abstract

By the generalized linear quantum transformation theory, we concisely derive the analytic expressions of partition function for general quadratic systems of multi-mode boson and fermion Fock space without any information for the energy spectrum. Under a general condition, we firstly acquire the exact expressions of energy spectra for these systems.

DOI
10.1088/0253-6102/31/1/121

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By the generalized linear quantum transformation theory, we concisely derive the analytic expressions of partition function for general quadratic systems of multi-mode boson and fermion Fock space without any information for the energy spectrum. Under a general condition, we firstly acquire the exact expressions of energy spectra for these systems.
We construct a general supersymmetric quantum transformation for studying the supersymmetric quadratic Hamiltonian which contains the interaction of multi-mode fermions with multi-mode bosons. The Hamiltonian can be derived from that of multi-mode radiation field interacting with m two-level atoms. By using the supersymmetric quantum transformation, the diagonolized Hamiltonian is given. We also concisely derive the analytic expression of the super-partition function for the supersymmetric quadratic Hamiltonian without knowing the energy spectrum.
Making use of the transformation relation between the ordinary form and the antinormal product form of boson exponential quadratic operators (BEQO's), we present an effective method which can be conveniently used to calculate arbitrary matrix elements of BEQO's. By this method, some important matrix elements have been calculated analytically. As a preliminary application, we obtain the exact solution of the density matrix and partition function for the general boson quadratic Hamiltonian without any information for the energy level. As a natural extension, we also obtain the partition function for a general fermion quadratic system.