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宇称时间对称性声学

Parity-time symmetric acoustics

  • 摘要: 对称性是自然界中最基本的物理属性之一。很多物理现象都与对称性相关联。例如,量子力学中描述具备一定对称性微观物理过程采用厄米—哈密顿算符,其中厄米性不仅确保算符本征值为实数,而且使微观过程满足几率守恒。1998年,Bender和Boettcher发现存在一类非厄米—哈密顿算符,它们的本征值也为实数并满足几率守恒。这类非厄米哈密顿算符最为典型的特征是满足宇称时间对称性。由于时变薛定谔方程和近轴波动方程形式具有相似性,故可进一步将宇称时间对称性引入经典波开放体系。文章回顾了量子体系中宇称时间对称破缺的发现过程,介绍了宇称时间对称性声学的理论模型,以及近期发现的一些奇异效应,并展望了宇称时间对称性声学的研究前景。

     

    Abstract: Symmetries are one of the most fundamental properties of nature, and are the basis of many physical phenomena. For example, in quantum mechanics the Hermitian Hamiltonian is employed to describe the microscopic processes that obey certain symmetries, where the Hermitian ensures not only purely real spectra of operators but also conservation of probability. In 1998,Bender and Boettcher found that the non-Hermitian Hamiltonians that respect parity (P) and time(T) symmetry might have the same properties. Since the time-dependent Schrödinger equation and paraxial wave equation are similar in form, it is possible to extend the PT symmetry into classical wave open systems. In this article, we first review the discovery of PT symmetry breaking in quantum systems. Then we introduce the theory of PT-symmetric acoustics, describe certain recent experimental observations that include some very intriguing effects, and discuss the future prospects of this rising field.

     

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