二次型法处理量子模型  

Quadratic Form Method for DealingwithQuantumModels

作　　者：陈洪宇 杨双良 吕东燕[1] 周骁[1] 周原[1] CHEN Hong-yu;YANG Shuang-liang;LV Dong-yan;ZHOU Xiao;ZHOU Yuan(School of Mathematics,Physics and Optoelectronic Engineering,Hubei University of Automotive Technology,Shiyan 442002,China)

机构地区：[1]湖北汽车工业学院数理与光电工程学院,湖北十堰442002

出　　处：《量子光学学报》2023年第2期16-22,共7页Journal of Quantum Optics

基　　金：国家自然科学基金(11774285,11774282);湖北省自然科学基金(2020CFB748);山东省自然科学基金(ZR2021MA042,ZR2021MA078)。

摘　　要：为提出一种更加简便有效的对角化哈密顿量的实用方法,以线性代数中的N元二次型的通用计算流程为基础,研究了二重构型类的量子玻色模型的哈密顿量对角化方法。以Dicke模型及腔光力杂化体系的哈密顿量的对角化过程为例,通过普通二次型到标准二次型的线性代数计算流程验证了该方法的正确性和有效性。尽管应用此法来处理量子模型的哈密顿量对角化问题有二重构型的条件限制,但是相信它也会为研究特定体系的量子相变问题提供另一类行之有效且简便的基本方法。In order to put forward a more convenient,effective,and practical method of diagonalizing Hamiltonian,the exact diagonalization of the Hamiltonian of the quantum boson model can be achieved through a general computation process in linear algebra,namely the N-ary quadratic form.Taking the Dicke model and the optomechanical hybrid system for example,the accuracy and effectiveness of this proposed method are verified through the linear algebra calculation process from the ordinary quadratic form to the standard quadratic one.Although this method is constrained by the second-order configuration for dealing with the Hamiltonian diagonalization,it is also believed to be able to provide another basic and effective method for studying the quantum phase transitions for some special systems.

关 键 词：量子光学 哈密顿量对角化 二次型 本征能量 

分 类 号：O431.2[机械工程—光学工程]