Braid Group and Topological Phase Transitions in Nonequilibrium Stochastic Dynamics
Mesoscale and Nanoscale Physics
2013-05-23 v2 Disordered Systems and Neural Networks
Statistical Mechanics
Abstract
We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.
Cite
@article{arxiv.1212.4241,
title = {Braid Group and Topological Phase Transitions in Nonequilibrium Stochastic Dynamics},
author = {Jie Ren and N. A. Sinitsyn},
journal= {arXiv preprint arXiv:1212.4241},
year = {2013}
}
Comments
4+ pages, 4 figures, published in PRE as a Rapid Communication. See http://pre.aps.org/abstract/PRE/v87/i5/e050101