Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

Abstract

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

19 pages, 8 figures, 8 appendices; two-column format; published article freely available until November 1, 2017, via the link https://authors.elsevier.com/a/1ViuB_55BgJ2g

References in corpus (18)

• Making Sense of Non-Hermitian Hamiltonians
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Observation of bound states in Lieb photonic lattices
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Periodically driven Quantum Ratchets: Symmetries and Resonances
• Rectification of laser-induced electronic transport through molecules
• Light transport in PT-invariant photonic structures with hidden symmetries
• Impact of loss on the wave dynamics in photonic waveguide lattices
• Coupled Oscillator Systems Having Partial PT Symmetry
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Non-Hermitian tight-binding network engineering
• Invariants of broken discrete symmetries
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• Bloch dynamics in lattices with long range hoppings
• Local symmetries in one-dimensional quantum scattering
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• Non-Local Currents and the Structure of Eigenstates in Planar Discrete Systems with Local Symmetries
• Exposing local symmetries in distorted driven lattices via time-averaged invariants

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