Transparent lattices and their solitary waves

TL;DR

This paper introduces a new class of transparent lattice models with non-trivial potentials and site-dependent hopping, using supersymmetric quantum mechanics, and identifies their potentials as solitary waves, with potential applications in electromagnetic and quantum systems.

Contribution

It generalizes supersymmetric quantum mechanics to discrete variables to construct transparent lattice models with solitary wave solutions.

Findings

Identified a biparametric family of potentials and hopping functions as solitary waves.

Developed a formalism involving a finite-difference Darboux transformation.

Proposed feasible implementations in electromagnetic and quantum systems.

Abstract

We provide a familiy of transparent tight-binding models with non-trivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.