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

Abstract

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

6 pages, 6 figures

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Cited by in corpus (8)

• Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory
• Comprehensive understanding of parity-time transitions in $\mathcal{P}\mathcal{T}$ symmetric photonic crystals with an antiunitary group theory
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• "Striped" Rectangular Rigid Box with Hermitian and non-Hermitian $\mathcal{P}\mathcal{T}$ Symmetric Potentials