Local perturbations of potential well arrays

Abstract

We consider an equidistant array of disjoint potential wells in ${\mathbb{R}}^{\nu }$, $\nu \ge 2$, built over a straight line, and show that, under a restriction on the potential support aspect ratio, a perturbation consisting of longitudinal shifts of a finite number of them preserving the disjointness gives rise to a non-empty discrete spectrum below the threshold of the lowest spectral band.