PT-symmetric lattices with spatially extended gain/loss are generically unstable

Abstract

We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a parabolic real potential with a linear imaginary part and the cases of no real and constant or linear imaginary potentials. On the other hand, this instability can be avoided and the spectrum can be real for localized or compact PT-symmetric potentials. The linear lattices are analyzed through discrete Fourier transform techniques complemented by numerical computations.

6 pages, 4 figures

References in corpus (20)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
• Experimental Study of Active LRC Circuits with PT-Symmetries
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Stability analysis for solitons in PT-symmetric optical lattices
• Solitons in PT-symmetric nonlinear lattices
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Stability of solitons in PT-symmetric couplers
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances
• Nonlinear modes in finite-dimensional PT-symmetric systems
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• PT-Symmetric Oligomers: Analytical Solutions, Linear Stability and Nonlinear Dynamics
• Nonlinear modes in the harmonic PT-symmetric potential
• Solitons in a chain of PT-invariant dimers
• Stability of localized modes in PT-symmetric nonlinear potentials
• Stabilization of solitons in PT models with supersymmetry by periodic management
• Discrete solitons in PT-symmetric lattices
• Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer
• Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

Cited by in corpus (10)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• The Dissipative Bose-Hubbard Model. Methods and Examples
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Nonlinear dynamics in PT-symmetric lattices
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• Nonlinear modes in a generalized $\mathcal{P}\mathcal{T}$-symmetric discrete nonlinear Schrödinger equation
• Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
• PT-symmetry breaking with divergent potentials: lattice and continuum cases
• Interplay of fractionality and $\mathcal{P}\mathcal{T}$- symmetry on a 1D lattice
• Existence and stability of PT-symmetric vortices in nonlinear two-dimensional square lattices