Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
Personal tools
Log in

Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes

Oliver Bendix, Ragnar Fleischmann, Tsampikos Kottos, and Boris Shapiro (2009)

Phys. Rev. Lett. 103(3):030402.  ( BibTeX export )

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_PT~min{delta}, thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma_PT~1/N^2 and the distribution P(gamma_PT) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.