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Geometric Phases for Three State Systems

Mark S. Byrd
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Abstract

The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would appear in a three dimensional quantum system with adiabatic characteristics are given explicitly. This is done in terms of the Euler angle parameterization of SU(3) which enables a straight-forward calculation of these quantities and its immediate generalization.

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Mark S. Byrd. 1999-02-17. Geometric Phases for Three State Systems. https://arxiv.org/abs/quant-ph/9902061

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