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arXiv · 1510.01014

Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions

Kaustubh S. Agarwal·Rajeev K. Pathak·Yogesh N. Joglekar
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Abstract

Non-hermitian, $\mathcal{PT}$-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, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.

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Kaustubh S. Agarwal, Rajeev K. Pathak, Yogesh N. Joglekar. 2015-10-05. Exactly solvable $\mathcal{PT}$-symmetric models in two dimensions. https://doi.org/10.1209/0295-5075/112/31003

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