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American Journal of Physics

Multiple time scale methods for adiabatic systems

James Lee Anderson

Published Oct 1, 1992• 7 citations
Publisher

Abstract

The method of multiple time scales is applied to adiabatic systems. Adiabatic theorems for both classical and quantum systems are derived and expressions for Berry’s phase and its classical counterpart are obtained within the framework of a consistent approximation scheme.
DOI
10.1119/1.17016

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The higher-order adiabatic approximation method of solving the Schr\"odinger equation for slowly transported quantum systems, which contains Berry's improved adiabatic theorem as its zeroth-order step, is generalized to solve evolution equations for a wide class of slowly transported classical systems. It is shown how the adiabatic condition is broken and transitions between different modes take place. Selection rules for such transitions are shown to be a topological property of the evolution path in parameter space.
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