Transparent lattices and their solitary waves

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.

10 pages, 6 figures

References in corpus (6)

• Tunable gauge potential for neutral and spinless particles in driven lattices
• 39-K Bose-Einstein condensate with tunable interactions
• Coherent Quantum Transport in Photonic Lattices
• Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene
• Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures
• Playing relativistic billiards beyond graphene