Adiabatic Perturbation Theory and Geometric Phases for Degenerate Systems
Quantum Physics
2015-05-18 v2
Abstract
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for degenerate systems. The same formalism can be used to find non-adiabatic corrections to the non-Abelian Wilczek-Zee geometric phase. These corrections are relevant to assess the validity of the practical implementation of the concept of fractional exchange statistics. We illustrate the formalism by exactly solving a time-dependent problem and comparing its solution to the perturbative one.
Keywords
Cite
@article{arxiv.1001.5255,
title = {Adiabatic Perturbation Theory and Geometric Phases for Degenerate Systems},
author = {Gustavo Rigolin and Gerardo Ortiz},
journal= {arXiv preprint arXiv:1001.5255},
year = {2015}
}
Comments
5 pages, no figures, RevTex4; v2: published version