PT-symmetry breaking with divergent potentials: lattice and continuum cases

Abstract

We investigate the parity- and time-reversal ($\mathcal{P}\mathcal{T}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\mathcal{P}\mathcal{T}$-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile $\mathcal{P}\mathcal{T}$ threshold for an open finite lattice, we show that continuum loss-gain potentials $V_{\alpha }(x)\propto i|x{|}^{\alpha }\mathrm{sign}(x)$ have a positive $\mathcal{P}\mathcal{T}$-breaking threshold for $\alpha >-2$, and a zero threshold for $\alpha \le -2$. When $\alpha <0$ localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of $\mathcal{P}\mathcal{T}$-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the $\mathcal{P}\mathcal{T}$-symmetry broken region.

Revised text

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Cited by in corpus (9)

• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Non-Hermitian tight-binding network engineering
• Scattering properties of PT-symmetric layered periodic structures
• Bound states in the continuum in a two-dimensional PT-symmetric system
• Veiled symmetry of disordered Parity-Time lattices: protected PT-threshold and the fate of localization
• Parity-time symmetry under magnetic flux
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• 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