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Chinese Physics C

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLYCHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR

Chen Sun

Published Jan 1, 1988• 0 citations
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Abstract

By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.

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Chinese Physics C•Jan 1, 1989•0 citations
By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.
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Considering that the classical evolution equations are similar to the Schrodinger eqaution, we point out that there is the structure of the Berry's Phase in the solution of a classical evolution eqaution with adiabatic changing parameters. Thus, we can use a classical evolution process to imitate the quantum adiabatic process. As an example, the motion of a charged particle in slowly-changing magnetic field is studied and the corresponding phase factor can be interpreted as a holomony of the fiber bundle on the sphare s~2 in the parameter space.