Battelli, F and Diblík, J and Fečkan, M and Pickton, J and Pospíšil, M and Susanto, H (2015) Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss. Nonlinear Dynamics, 81 (1-2). pp. 353-371. DOI https://doi.org/10.1007/s11071-015-1996-2
Battelli, F and Diblík, J and Fečkan, M and Pickton, J and Pospíšil, M and Susanto, H (2015) Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss. Nonlinear Dynamics, 81 (1-2). pp. 353-371. DOI https://doi.org/10.1007/s11071-015-1996-2
Battelli, F and Diblík, J and Fečkan, M and Pickton, J and Pospíšil, M and Susanto, H (2015) Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss. Nonlinear Dynamics, 81 (1-2). pp. 353-371. DOI https://doi.org/10.1007/s11071-015-1996-2
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.
Item Type: | Article |
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Additional Information: | submitted (2014) |
Uncontrolled Keywords: | PT-symmetry; PT-reversibility; Schrodinger equation; Melnikov function; Perturbation; Chaos |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 02 Jul 2015 19:26 |
Last Modified: | 30 Oct 2024 20:22 |
URI: | http://repository.essex.ac.uk/id/eprint/14219 |
Available files
Filename: 1412.0164v1.pdf