Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss

F. Battelli, J. Diblík, M. Fečkan, J. Pickton, M. Pospíšil, H. Susanto

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8 Scopus citations

Abstract

A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.

Original languageBritish English
Pages (from-to)353-371
Number of pages19
JournalNonlinear Dynamics
Volume81
Issue number1-2
DOIs
StatePublished - 10 Jul 2015

Keywords

  • Chaos
  • Melnikov function
  • Perturbation
  • PT-reversibility
  • PT-symmetry
  • Schrödinger equation

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