PT-symmetry breaking with divergent potentials: Lattice and continuum cases

Yogesh N. Joglekar, Derek D. Scott, and Avadh Saxena
Phys. Rev. A 90, 032108 – Published 17 September 2014

Abstract

We investigate the parity- and time-reversal (PT-) symmetry breaking in lattice models in the presence of long-ranged, non-Hermitian, PT-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile PT threshold for an open finite lattice, we show that continuum loss-gain potentials Vα(x)i|x|αsgn(x) have a positive PT-breaking threshold for α>2, and a zero threshold for α2. When α<0 localized states with complex (conjugate) energies in the continuum energy band occur at higher loss-gain strengths. We investigate the signatures of PT-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time scale in the PT-symmetry broken region.

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  • Received 17 March 2014
  • Revised 7 July 2014

DOI:https://doi.org/10.1103/PhysRevA.90.032108

©2014 American Physical Society

Authors & Affiliations

Yogesh N. Joglekar1, Derek D. Scott1, and Avadh Saxena2

  • 1Department of Physics, Indiana University Purdue University, Indianapolis (IUPUI), Indianapolis, Indiana 46202, USA
  • 2Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA

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Vol. 90, Iss. 3 — September 2014

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