二态量子系统准确布居动力学的一类新型相空间表示及其与三角窗函数的关系  

A Novel Class of Phase Space Representations for the Exact Population Dynamics of Two-State Quantum Systems and the Relation to Triangle Window Functions

作　　者：程祥松 贺鑫 刘剑[1] Xiangsong Cheng;Xin He;Jian Liu(Beijing National Laboratory for Molecular Sciences,Institute of Theoretical and Computational Chemistry,College of Chemistry and Molecular Engineering,Peking University,Beijing 100871,China)

机构地区：[1]北京大学化学与分子工程学院,北京分子科学国家研究中心,理论与计算化学研究所,北京100871

出　　处：《Chinese Journal of Chemical Physics》2024年第2期230-254,I0102,共26页化学物理学报（英文）

摘　　要：二态系统是最简单的且无经典对应的量子系统,对二态系统的同构表示的认识和研究能启发研究人员对其动力学与统计行为的更深刻理解.本文使用在[J.Chem.Phys.145,204105(2016);J.Chem.Phys.151,024105(2019);J.Phys.Chem.Lett.12,2496(2021)]等文章中发展的约束相空间严格理论、非协变相空间函数、含时权重函数与含时归一化因子来构建一类新型量子相空间表示.这类同构表示可以导出二态量子系统布居动力学的准确结果.约束相空间上的轨迹运动方程同构于含时薛定谔方程.每条相空间轨迹对于布居动力学所对应积分表达式的贡献严格半正定。进一步证明了在[J.Chem.Phys.145,144108(2016)]这篇文章中根据经验提出的三角窗函数方法在本质上可以对应于本文的这类新型相空间表示的一个特殊情况,因此同样是二态量子系统准确布居动力学的同构表示.Isomorphism of the two-state system is heuristic in understanding the dynamical or statistical behavior of the simplest yet most quantum system that has no classical counterpart.We use the constraint phase space developed in J.Chem.Phys.145,204105(2016);151,024105(2019);J.Phys.Chem.Lett.12,2496(2021),non-covariant phase space functions,time-dependent weight functions,and time-dependent normalization factors to construct a novel class of phase space representations of the exact population dynamics of the two-state quantum system.The equations of motion of the trajectory on constraint phase space are isomorphic to the time-dependent Schrödinger equation.The contribution of each trajectory to the integral expression for the population dynamics is always positive semi-definite.We also prove that the triangle window function approach,albeit proposed as a heuristic empirical model in J.Chem.Phys.145,144108(2016),is related to a special case of the novel class and leads to an isomorphic representation of the exact population dynamics of the two-state quantum system.

关 键 词：相空间表示 约束相空间 有限态量子系统 二态系统 布居动力学 

分 类 号：O643.1[理学—物理化学] O644.1[理学—化学]