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Title: Geometry of time-dependent PT -symmetric quantum mechanics
Authors: Zhang, DJ
Wang, QH 
Gong, J 
Issue Date: 1-Oct-2021
Publisher: IOP Publishing
Citation: Zhang, DJ, Wang, QH, Gong, J (2021-10-01). Geometry of time-dependent PT -symmetric quantum mechanics. Chinese Physics B 30 (10) : 105202-105202. ScholarBank@NUS Repository.
Abstract: A new type of quantum theory known as time-dependent PT -symmetric quantum mechanics has received much attention recently. It has a conceptually intriguing feature of equipping the Hilbert space of a PT -symmetric system with a time-varying inner product. In this work, we explore the geometry of time-dependent PT -symmetric quantum mechanics. We find that a geometric phase can emerge naturally from the cyclic evolution of a PT -symmetric system, and further formulate a series of related differential-geometry concepts, including connection, curvature, parallel transport, metric tensor, and quantum geometric tensor. These findings constitute a useful, perhaps indispensible, tool to investigate geometric properties of PT -symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometric phase [Phys. Rev. Lett. 91 187902 (2003)], which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase unveiled in this work.
Source Title: Chinese Physics B
ISSN: 1674-1056
DOI: 10.1088/1674-1056/ac0521
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