title: Transparent lattices and their solitary waves.
abstract: We provide a family of transparent tight-binding models with nontrivial 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.
authors.affiliation: Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, México.
authors.forename: E
authors.initials: E
authors.lastname: Sadurní
mesh_terms: D055590:Electromagnetic Phenomena; D005240:Feasibility Studies; D008962:Models, Theoretical; D009038:Motion; D011789:Quantum Theory