A topological formulation for exotic quantum holonomy
https://doi.org/10.17586/2220-8054-2015-6-6-786-792
Abstract
An adiabatic change of parameters along a closed path may interchange the (quasi-)eigenenergies and eigenspaces of a closed quantum system. Such discrepancies, induced by adiabatic cycles are referred to as the exotic quantum holonomy, which is an extension of the geometric phase. \Small" adiabatic cycles induce no change on eigenspaces, whereas some \large" adiabatic cycles interchange eigenspaces. We explain the topological formulation for the eigenspace anholonomy, where the homotopy equivalence precisely distinguishes the larger cycles from smaller ones. An application to two level systems is explained. We also examine the cycles that involve the adiabatic evolution across an exact crossing, and the diabatic evolution across an avoided crossing. The latter is a nonadiabatic example of the exotic quantum holonomy.
Supporting agencies: This research was supported by the Japan Ministry of Education, Culture, Sports, Science and Technology under the Grant number 15K05216.
About the Authors
A. Tanaka
Department of Physics, Tokyo Metropolitan University
Japan
Japan
Hachioji, Tokyo 192-0397
T. Cheon
Laboratory of Physics, Kochi University of Technology
Japan
Japan
Tosa Yamada, Kochi 782-8502
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Review
For citations:
Tanaka A., Cheon T. A topological formulation for exotic quantum holonomy. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(6):786-792. https://doi.org/10.17586/2220-8054-2015-6-6-786-792
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