Geometry of time-dependent $mathcal{PT}$-symmetric quantum mechanics |
| |
Affiliation: | 1.Department of Physics, Shandong University, Jinan 250100, China;2.Department of Physics, National University of Singapore, 117551, Singapore |
| |
Abstract: | A new type of quantum theory known as time-dependent $mathcal{PT}$-symmetric quantum mechanics has received much attention recently. It has a conceptually intriguing feature of equipping the Hilbert space of a $mathcal{PT}$-symmetric system with a time-varying inner product. In this work, we explore the geometry of time-dependent $mathcal{PT}$-symmetric quantum mechanics. We find that a geometric phase can emerge naturally from the cyclic evolution of a $mathcal{PT}$-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 $mathcal{PT}$-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. |
| |
Keywords: | time-dependent $mathcal{PT}$-symmetric quantum mechanics geometry time-varying inner product unconventional geometric phase |
|
| 点击此处可从《中国物理 B》浏览原始摘要信息 |
|
点击此处可从《中国物理 B》下载免费的PDF全文 |
|