Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
Other Condensed Matter
2009-09-02 v1 Disordered Systems and Neural Networks
Quantum Physics
Abstract
We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasi-degenerate levels with splitting delta exp{-N/xi}, where \xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma min(delta), thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma (1/N)^2 and the distribution P(gamma) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
Keywords
Cite
@article{arxiv.0908.2380,
title = {Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes},
author = {Oliver Bendix and Ragnar Fleischmann and Tsampikos Kottos and Boris Shapiro},
journal= {arXiv preprint arXiv:0908.2380},
year = {2009}
}