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Journal of Physics A Mathematical and General

Berry's phase in a moving boundary problem

O Kwon, Y Kim, C Lee

Published Nov 21, 1992• 7 citations
Publisher

Abstract

For a system in a well with a moving boundary the authors show that the s system memorizes the history of motion of the boundary through a non-integrable phase factor, Berry's phase. They first treat the case that the transformed Hamiltonian has a constant frequency. Secondly, in the case of time-dependent frequency they discuss non-adiabatic and non-cyclic cases.

DOI
10.1088/0305-4470/25/22/032

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Modern Physics Letters B•Jun 17, 2014•2 citations
For a system in a well with a moving boundary the authors show that the s system memorizes the history of motion of the boundary through a non-integrable phase factor, Berry's phase. They first treat the case that the transformed Hamiltonian has a constant frequency. Secondly, in the case of time-dependent frequency they discuss non-adiabatic and non-cyclic cases.
Shows that (non-adiabatic) Berry phases in time-independent systems arise for fundamentally different reasons than those for time-dependent systems. For time-independent Hamiltonians the Berry phases are seen to only depend on the chosen cyclic initial state, the Hamiltonian merely providing the appropriate period. The author also discusses two time-dependent examples where the time dependence arises from different sources, namely a two-level atom in an intense laser and a harmonic oscillator with a periodic forcing term.
Using the Lewis-Riesenfeld′s quantum invariant theory,the Lewis-Riesenfeld phases for a time-dependent frequency harmonic oscillator,which is confined in an infinite well with a moving wall,are calculated.We find that the geometric part of the Lewis-Riesenfeld phases are identical with the “non-adiabatic Berry phases” described by D.Y.Liu in Acta Phys.Sin.It may be important that our results,at least for the system with a sinusoidally oscillating boundary,do not show any non-trivial Berry phase acquired.