PT Symmetric Aubry-Andre Model

Abstract

PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice sites. We obtain the Hofstadter Butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserves the total intensity.

References in corpus (6)

• PT-Symmetric Electronics
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• PT-Symmetric Wave Chaos
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Bypassing the bandwidth theorem with PT symmetry
• Light Transport in Random Media with $\mathcal{P}\mathcal{T}$-Symmetry

Cited by in corpus (43)

• Non-Hermitian Physics
• Topological phase transition in non-Hermitian quasicrystals
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• New topological invariants in non-Hermitian systems
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Topological phase in a non-Hermitian PT symmetric system
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Edge states at the interface of non-Hermitian systems
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Topological Phase Transition Independent of System Non-Hermiticity
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• PT Symmetric Floquet Topological Phase in SSH Model
• Stable topological edge states in a non-Hermitian four-band model
• Inversion symmetric non-Hermitian Chern insulator
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
• Quasiperiodic granular chains and Hofstadter butterflies
• Spontaneously Broken Particle-Hole Symmetry in Photonic Graphene with Gain and Loss
• Engineering Dissipative Quasicrystals
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• Non-Hermitian edge burst without skin localizations
• $\mathcal{P}\mathcal{T}$ symmetry of the Su-Schrieffer-Heeger model with imaginary boundary potentials and next-nearest-neighboring coupling
• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Universal Route for the Emergence of Exceptional Points in PT-Symmetric Metamaterials with Unfolding Spectral Symmetries
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Equivalence and superposition of real and imaginary quasiperiodicities
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Anderson localization induced by complex potential
• Pseudo PT symmetric lattice
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Transport characteristics of a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian system: Effect of environmental interaction
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Hofstadter's Cocoon
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems