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 nonempty discrete spectrum below the threshold of the lowest spectral band.

arXiv commentMinor improvements, typos corrected; to appear in Journal of Spectral Theory