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Chinese Physics C

BERRY'S PHASE FACTORS IN MOVING FRAMES OF REFERENCE AND THEIR OBSERVABLE EFFECTS

Chen Sun

Published Jan 1, 1990• 0 citations
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Abstract

Under non-relativistic conditions, the properties of adiabatic solutions of the Schrodinger equation in moving frame of reference and the behaviours of the corresponding Berry's Phase are analysed. Two cases of translation and rotation are discussed in detail, which show that the existence of Berry's phase depends on the choice of frame of reference. While Bitter and Dubbers's experiment is explained by the first-order approximation in our discussion, the nonadiabatic effects in this experiment are predicted by the second-order approximation when the adiabatic condition is broken.

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Under non-relativistic conditions, the properties of adiabatic solutions of the Schrodinger equation in moving frame of reference and the behaviours of the corresponding Berry's Phase are analysed. Two cases of translation and rotation are discussed in detail, which show that the existence of Berry's phase depends on the choice of frame of reference. While Bitter and Dubbers's experiment is explained by the first-order approximation in our discussion, the nonadiabatic effects in this experiment are predicted by the second-order approximation when the adiabatic condition is broken.
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Berry pointed out that the Aharonov-Bohm phase could be considered as a Berry phase.In his argument,he gave up the adiabatic approximation,and the nonstationarity of quantum states was not concerned.In this paper we re-investigate Berry’s proof,and find that his final statement is correct,and in his argument,the adiabatic approximation should be used.In the AB effect,a moving electron is described as a moving wave packet (nonstationary),and the appearance of AB phase originates from the requirement that the evolution of the wave packet must satisfy the Schrdinger equation.
A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.