Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models

Abstract

We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.

28 pages, 13 figures

References in corpus (11)

• Making Sense of Non-Hermitian Hamiltonians
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• PT-Symmetric Talbot Effects
• Invisibility and PT-symmetry
• Optical mesh lattices with PT-symmetry
• Breaking of PT-symmetry in bounded and unbounded scattering systems
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems

Cited by in corpus (16)

• Polarization-resolved microscopy through scattering media via wavefront shaping
• PT-symmetry breaking in the steady state of microscopic gain-loss systems
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-equilibrium magnetic phases in spin lattices with gain and loss
• Exceptional points of degeneracy and $\mathcal{P}\mathcal{T}$-symmetry in photonic coupled chains of scatterers
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Solitons in PT-symmetric ladders of optical waveguides
• PT-symmetric optical superlattices
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Transport and localization of waves in ladder-shaped lattices with locally $\mathcal{P}\mathcal{T}$-symmetric potentials
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations
• Double-sided unidirectional reflectivity
• PT-symmetric transport in non-PT-symmetric bi-layer optical arrays
• Physical relevance of time-independent scattering calculations in non-Hermitian systems: The role of time-growing bound states