Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes

Jul 17, 2009
4 pages
Published in:
  • Phys.Rev.Lett. 103 (2009) 030402
e-Print:

Citations per year

2009201320172021202502468
Abstract: (arXiv)
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.
  • 72.15.Rn
  • 11.30.Er
  • 42.82.Et
  • 03.65.-w