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理论物理通讯：英文版

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Xu, Xiu-Wei, Ren, Ting-Qi, Liu ., Shuyan, Ma, Qiu-Ming, Sheng-Dian

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

使用转变关系在之中平常，正常，和 antinormalordering 为多模式波色子指数的二次的多项式操作员(BEQPO “ s ) ，我们在场为 BEQPO 的任意的矩阵元素的分析表示” s。作为一个初步的应用程序，我们关于波色子获得分区功能的准确表达式二次的多项式系统，在粒子数字的矩阵元素，坐标，和动量表示，和为 BEQPO 的 P 表示“ s。

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使用转变关系在之中平常，正常，和 antinormalordering 为多模式波色子指数的二次的多项式操作员(BEQPO “ s ) ，我们在场为 BEQPO 的任意的矩阵元素的分析表示” s。作为一个初步的应用程序，我们关于波色子获得分区功能的准确表达式二次的多项式系统，在粒子数字的矩阵元素，坐标，和动量表示，和为 BEQPO 的 P 表示“ s。
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.
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.