𝒫𝒯-symmetric quantum mechanics

IF 45.9 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Reviews of Modern Physics Pub Date : 2024-10-28 DOI:10.1103/revmodphys.96.045002
Carl M. Bender, Daniel W. Hook
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Abstract

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a 𝒫𝒯-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of 𝒫𝒯-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of 𝒫𝒯 symmetry have been applied in the context of many different branches of physics. This review introduces the concepts of 𝒫𝒯 symmetry by focusing on elementary one-dimensional 𝒫𝒯-symmetric quantum and classical mechanics and relies, in particular, on oscillator models to illustrate and explain the basic properties of 𝒫𝒯-symmetric quantum theory.

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𝒫𝒯对称量子力学
一般认为,一个物理上可接受的量子系统(具有正定频谱并符合统一性要求的系统)的哈密顿必须是赫米托的。然而,一个𝒫𝒯对称哈密顿也可以定义一个物理上可接受的量子力学系统,即使哈密顿不是赫米特的。对𝒫𝒯对称量子系统的研究是理论物理学和实验物理学中一个年轻而极其活跃的研究领域。这篇综述的目的是为资深科学家和研究生提供该领域简明易读的介绍,使他们能够理解更高级的出版物,并开始自己的理论或实验研究活动。𝒫𝒯对称性的思想和技术已被应用于许多不同的物理学分支。这篇综述以基本的一维𝒫𝒯对称量子力学和经典力学为重点,介绍了𝒫𝒯对称性的概念,特别是依靠振荡器模型来说明和解释𝒫𝒯对称量子理论的基本性质。
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来源期刊
Reviews of Modern Physics
Reviews of Modern Physics 物理-物理:综合
CiteScore
76.20
自引率
0.70%
发文量
30
期刊介绍: Reviews of Modern Physics (RMP) stands as the world's foremost physics review journal and is the most extensively cited publication within the Physical Review collection. Authored by leading international researchers, RMP's comprehensive essays offer exceptional coverage of a topic, providing context and background for contemporary research trends. Since 1929, RMP has served as an unparalleled platform for authoritative review papers across all physics domains. The journal publishes two types of essays: Reviews and Colloquia. Review articles deliver the present state of a given topic, including historical context, a critical synthesis of research progress, and a summary of potential future developments.
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