A Unified Theory of Quantum Holonomies
Abstract
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.
Keywords
Cite
@article{arxiv.0902.2878,
title = {A Unified Theory of Quantum Holonomies},
author = {Atushi Tanaka and Taksu Cheon},
journal= {arXiv preprint arXiv:0902.2878},
year = {2010}
}
Comments
24pages; To be published in Ann. Phys. (N.Y.); Corrected typos