Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

Abstract

We investigate the effects of competition between two complex, $\mathcal{P}\mathcal{T}$-symmetric potentials on the $\mathcal{P}\mathcal{T}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and $V_{\xi }(x)=i\xi [\delta (x-a)-\delta (x+a)]$, represent long-range and localized gain/loss regions respectively. We obtain the $\mathcal{P}\mathcal{T}$-symmetric phase in the $(Z,\xi )$ plane, and find that for locations $\pm a$ near the edge of the box, the $\mathcal{P}\mathcal{T}$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $\mathcal{P}\mathcal{T}$-symmetry will be restored by increasing the strength $\xi$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $\mathcal{P}\mathcal{T}$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $\mathcal{P}\mathcal{T}$-symmetric potentials show unique, unexpected properties.

arXiv comment7 pages, 3 figures

References in corpus (19)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermitian Representation of Quantum Mechanics
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Must a Hamiltonian be Hermitian?
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• PT symmetric square well
• Robust and fragile PT-symmetric phases in a tight-binding chain
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Complex Correspondence Principle
• Gegenbauer-solvable quantum chain model
• PT-symmetric square well and the associated SUSY hierarchies
• An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
• Solvability and PT-symmetry in a double-well model with point interactions
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Decays of degeneracies in PT-symmetric ring-shaped lattices

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• $\mathcal{P}\mathcal{T}$-symmetry breaking in a Kitaev chain with one pair of gain-loss potentials
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Anomalous Faraday effect in a $\mathcal{P}\mathcal{T}$-symmetric dielectric slab
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Time invariant $\mathcal{P}\mathcal{T}$-product and phase locking in $\mathcal{P}\mathcal{T}$-symmetric lattice models
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry
• PT-symmetry enabled stable modes in multi-core fiber