Abstract
In contrast to the idealized scenario of perfect global symmetries that is notoriously elusive, local symmetries [1] abound in nature. Prominent examples include quasicrystals [2], macromolecules [3] and tailored photonic multilayer-systems [4]. Since the Hamiltonian of a locally symmetric system does, in general, not commute with the local symmetry operation, even though the potential remains invariant under the respective transformation, tracking the influence on a system's dynamics can be challenging. A promising approach is the non-local continuity formalism that can readily be applied to discrete systems governed by a Schrödinger equation [5]. It relates a non-local charge to the non-local boundary current in each symmetry domain. For arrangements without on-site asymmetry, the continuity equation reads Σ = , where ∂z is the derivative in propagation direction. In this vein, we can readily distinguish locally symmetric structures from both fully non-symmetric systems on the one hand, and globally symmetric structures on the other. Notably, an experimental demonstration of this continuity equation has remained elusive so far.
© 2019 IEEE
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