Density-Functional Theory for the Dicke Hamiltonian

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Vebjørn H. Bakkestuen, Mihály A. Csirik, Andre Laestadius, Markus Penz
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引用次数: 0

Abstract

A detailed analysis of density-functional theory for quantum-electrodynamical model systems is provided. In particular, the quantum Rabi model, the Dicke model, and a generalization of the latter to multiple modes are considered. We prove a Hohenberg–Kohn theorem that manifests the magnetization and displacement as internal variables, along with several representability results. The constrained-search functionals for pure states and ensembles are introduced and analyzed. We find the optimizers for the pure-state constrained-search functional to be low-lying eigenstates of the Hamiltonian and, based on the properties of the optimizers, we formulate an adiabatic-connection formula. In the reduced case of the Rabi model we can even show differentiability of the universal density functional, which amounts to unique pure-state v-representability.

迪克哈密顿的密度函数理论
详细分析了量子电动力学模型系统的密度泛函理论。特别地,考虑了量子Rabi模型、Dicke模型以及后者的多模推广。我们证明了一个将磁化和位移作为内变量的Hohenberg-Kohn定理,并给出了几个可表征性的结果。介绍并分析了纯态和系综的约束搜索泛函。我们发现纯态约束搜索泛函的优化器是哈密顿量的低特征态,并根据优化器的性质,给出了绝热连接公式。在拉比模型的简化情况下,我们甚至可以证明普遍密度泛函的可微性,这相当于唯一的纯态v-表征性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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