Tag H. Susanto

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

F. Battelli, J. Diblik, M. Feckan, J. Pickton, M. Pospisil, H. Susanto

A Parity-Time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger 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.

http://arxiv.org/abs/1412.0164
Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Classical Analysis and ODEs (math.CA); Optics (physics.optics)

On the integrability of PT-symmetric dimers

J. Pickton, H. Susanto

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time (PT) symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is shown that the models are integrable. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter.

http://arxiv.org/abs/1307.2788
Optics (physics.optics); Quantum Gases (cond-mat.quant-gas); Exactly Solvable and Integrable Systems (nlin.SI)