Spreading of the conception of permanent resonance to wave motions over lattices

TL;DR

This paper extends the concept of permanent resonance, previously discovered in spectral zone creation, to wave motions over lattices using a finite difference Schrödinger equation with local and nonlocal potentials.

Contribution

It generalizes the permanent resonance mechanism to discrete lattices and finite difference Schrödinger equations, proposing potential extensions to multidiagonal potentials.

Findings

Resonance mechanism applies to spectral zone creation in lattices.

Generalization to nonlocal potentials broadens the applicability.

Potential for extending formalism to multidiagonal potentials.

Abstract

Discovered by us [1] special (permanent) resonance mechanism of spectral zone creation in periodic structures is generalized to the case of discrete space lattices and finite difference Schroedinger equation with local V(n) and minimally nonlocal U(n). It would be interesting to generalize the periodicity formalism to the multidiagonal finite-difference potentials.