Geometry of time-dependent PT-symmetric quantum mechanics

作     者：Da-Jian Zhang Qing-hai Wang Jiangbin Gong 张大剑;王清海;龚江滨

作者机构：Department of PhysicsShandong UniversityJinan 250100China Department of PhysicsNational University of Singapore117551Singapore 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2021年第30卷第10期

页      面：47-55页

核心收录：

学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 070205[理学-凝聚态物理] 08[工学] 0702[理学-物理学] 

基　　金：supported by Singapore Ministry of Education Academic Research Fund Tier I(WBS No.R-144-000-353-112) by the Singapore NRF Grant No.NRFNRFI2017-04(WBS No.R-144-000-378-281) supported by Singapore Ministry of Education Academic Research Fund Tier I(WBS No.R-144-000-352-112) 

主　　题：time-dependent𝒫PT-symmetric quantum mechanics geometry time-varying inner product unconventional geometric phase 

摘      要：A new type of quantum theory known as time-dependent𝒫PT-symmetric quantum mechanics has received much attention *** has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-symmetric system with a time-varying inner *** this work,we explore the geometry of time-dependent𝒫𝒯PT-symmetric quantum *** 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 *** findings constitute a useful,perhaps indispensible,tool to investigate geometric properties of𝒫PT-symmetric systems with time-varying system’s *** exemplify the application of our findings,we show that the unconventional geometric phase[***.91187902(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.