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The consistency of the adiabatic and exact geometric phases. (English) Zbl 1152.81850

Summary: With the help of the time-dependent gauge transformation, by which a set of time-invariant eigenstates of the Hamiltonian can be obtained, the geometric phase of the time-dependent system is obtained analytically. In the limit of the adiabatic condition, this phase exactly reduces to the adiabatic geometric phase. To illustrate the present theory, two solvable time-dependent systems are considered.

MSC:

81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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