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arXiv · 1406.4906

Transparent lattices and their solitary waves

E. Sadurní
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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.

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E. Sadurní. 2014-09-10. Transparent lattices and their solitary waves. https://doi.org/10.1103/physreve.90.033205

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