Geometry of time-dependent PT-symmetric quantum mechanics

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

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：0711[理学-系统科学] 07[理学] 070205[理学-凝聚态物理] 0703[理学-化学] 0701[理学-数学] 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 recently.It has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-symmetric system with a time-varying inner product.In this work,we explore the geometry of time-dependent𝒫𝒯PT-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 of𝒫PT-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.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.