Non-Local Currents and the Structure of Eigenstates in Planar Discrete Systems with Local Symmetries

Abstract

Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates.

17 pages, 7 figures

References in corpus (3)

• Observation of bound states in Lieb photonic lattices
• Invariants of broken discrete symmetries
• Local symmetries in one-dimensional quantum scattering

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