Explicit model checking algorithms explore the full state space of a system. State spaces are usually treated as directed graphs without any specific features. We gather a large collection of state spaces and extensiv...
详细信息
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-symmetri...
详细信息
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.
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