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arXiv · 0908.2380

Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes

Oliver Bendix·Ragnar Fleischmann·Tsampikos Kottos·Boris Shapiro
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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 ξis 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.

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Oliver Bendix, Ragnar Fleischmann, Tsampikos Kottos, Boris Shapiro. 2009-08-17. Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes. https://doi.org/10.1103/physrevlett.103.030402

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