Publication detail

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

BATTELLI, F. DIBLÍK, J. FEČKAN, M. PICKTON, J. POSPÍŠIL, M. SUSANTO, H.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original 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 ofmotion. 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.

English 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 ofmotion. 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.

Keywords

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

RIV year

2015

Released

11.06.2015

ISBN

0924-090X

Periodical

NONLINEAR DYNAMICS

Year of study

81

Number

1

State

US

Pages from

353

Pages to

371

Pages count

19

Documents

BibTex


@article{BUT114839,
  author="Flaviano {Battelli} and Josef {Diblík} and Michal {Fečkan} and John {Pickton} and Michal {Pospíšil} and Hadi {Susanto}",
  title="Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss",
  annote="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 ofmotion. 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.",
  chapter="114839",
  doi="10.1007/s11071-015-1996-2",
  howpublished="print",
  number="1",
  volume="81",
  year="2015",
  month="june",
  pages="353--371",
  type="journal article in Web of Science"
}