A Unified Theory of Quantum Holonomies

Details A Unified Theory of Quantum Holonomies A Unified Theory of Quantum Holonomies

2009-02-17

arxiv.org/abs/0902.2878v2

Annals Phys.324:1340-1359,2009

Physics

Quantum Physics

24pages; To be published in Ann. Phys. (N.Y.); Corrected typos

Scientific paper

10.1016/j.aop.2009.03.006

A periodic change of slow environmental parameters of a quantum system induces quantum holonomy. The phase holonomy is a well-known example. Another is a more exotic kind that exhibits eigenvalue and eigenspace holonomies. We introduce a theoretical formulation that describes the phase and eigenspace holonomies on an equal footing. The building block of the theory is a gauge connection for an ordered basis, which is conceptually distinct from Mead-Truhlar-Berry's connection and its Wilczek-Zee extension. A gauge invariant treatment of eigenspace holonomy based on Fujikawa's formalism is developed. Example of adiabatic quantum holonomy, including the exotic kind with spectral degeneracy, are shown.

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