Exactly solvable -symmetric models in two dimensions
1 Department of Physics, Savitribai Phule Pune University - Ganeshkhind, Pune 411007, Maharashtra, India
2 Department of Physics, Indiana University-Purdue University Indianapolis (IUPUI) - Indianapolis, IN 46202, USA
Received: 5 October 2015
Accepted: 5 November 2015
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.
PACS: 11.30.Er – Charge conjugation, parity, time reversal, and other discrete symmetries / 03.65.Ge – Solutions of wave equations: bound states / 42.82.Et – Waveguides, couplers, and arrays
© EPLA, 2015