Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve
Statistical Mechanics
2009-11-13 v2 Mesoscale and Nanoscale Physics
Abstract
We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the 3D-Minkovsky space. We also show that this geometric phase is responsible for the anholonomy effects in stochastic processes considered in [N. A. Sinitsyn and I. Nemenman, EPL {\bf 77}, 58001 (2007)], and use it to derive the stochastic system response to periodic parameter variations.
Keywords
Cite
@article{arxiv.0807.3121,
title = {Geometric phase for non-Hermitian Hamiltonian evolution as anholonomy of a parallel transport along a curve},
author = {N. A. Sinitsyn and Avadh Saxena},
journal= {arXiv preprint arXiv:0807.3121},
year = {2009}
}
Comments
10 pages 2 figures