Analytic calculation of arbitrary matrix elements for the boson exponential quadratic operator

Abstract

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.