2018/11/12 by Da-Jian Zhang, Zhang, Da-Jian, Qinghai Wang +3
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1811.04640
openalex publication_date 2018/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Time-dependent PT-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of time-dependent PT-symmetric quantum mechanics. We not only find a geometric phase factor emerging naturally from cyclic evolutions of PT-symmetric systems, but also formulate a series of differential geometry concepts, including connection, curvature, parallel transport, metric tensor, and quantum geometric tensor. Our findings constitute a useful, perhaps indispensible, tool to tackle physical problems involving PT-symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometrical phase [Phys. Rev. Lett. 91, 187902 (2003)], consisting of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase identified in this work.