Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions
Quantum Physics
2015-12-17 v1 Quantum Gases
Abstract
Non-hermitian, -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, potentials for a non-relativistic particle confined in a circular geometry. We show that the symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that breaking in two dimensions has a rich phase diagram, with multiple re-entrant symmetric phases.
Cite
@article{arxiv.1510.01014,
title = {Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions},
author = {Kaustubh S. Agarwal and Rajeev K. Pathak and Yogesh N. Joglekar},
journal= {arXiv preprint arXiv:1510.01014},
year = {2015}
}
Comments
6 pages, 6 figures