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Phase-space approach to Berry's phases

Dariusz Chruscinski
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Abstract

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light into the correspondence between classical and quantum adiabatic phases -- both phases are related with the averaging procedure: Hannay's angle with averaging over the classical torus and Berry's phase with averaging over the entire classical phase space with respect to the corresponding Wigner function. Generalizations to the non-abelian Wilczek--Zee case and mixed states are also included.

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Dariusz Chruscinski. 2004-06-04. Phase-space approach to Berry's phases. https://arxiv.org/abs/quant-ph/0406026

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