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Communications in Theoretical Physics

Linear Quantum Transformation Theory of Multi-Mode Bosons and Its Application to Calculation of Partition Function

Sixia Yu, Yong-De Zhang

Published Sep 15, 1995• 11 citations
Publisher

Abstract

In this paper, we present a linear quantum transformation theory in the -mode boson Fock space, and give a formula that shows how a transformation operator changes its exponential form to its normal ordered form. As an application we evaluate the partition function of a general quadratic system without any information of the energy levels of the system by using our transformation theory.

DOI
10.1088/0253-6102/24/2/185

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In this paper, we present a linear quantum transformation theory in the -mode boson Fock space, and give a formula that shows how a transformation operator changes its exponential form to its normal ordered form. As an application we evaluate the partition function of a general quadratic system without any information of the energy levels of the system by using our transformation theory.
By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.