Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes

Details Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes

2009-08-17

arxiv.org/abs/0908.2380v1

Phys.Rev.Lett.103:030402,2009

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevLett.103.030402

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.

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