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arXiv · 1302.0456

Aharonov-Bohm effect and geometric phases -- Exact and approximate topology

Kazuo Fujikawa
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Abstract

By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is characterized by the singularity associated with possible level crossing, is trivial in a precise sense. This topology of the geometric phase is quite different from the topology of the Aharonov-Bohm effect, where the topology is specified by the external local gauge field and it is exact for the slow as well as for the fast motion of the electron.

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Kazuo Fujikawa. 2013-02-03. Aharonov-Bohm effect and geometric phases -- Exact and approximate topology. https://doi.org/10.1142/9789814472906_0016

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