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arXiv · 1612.01798

Discrete spectrum of interactions concentrated near conical surfaces

Thomas Ourmières-Bonafos·Konstantin Pankrashkin
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Abstract

We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schr\"odinger operators with attractive $\delta$-interactions supported by infinite cones. Under the assumption that the cones have smooth cross-sections, we prove that such operators have infinitely many eigenvalues accumulating below the threshold of the essential spectrum and we express the accumulation rate in terms of the eigenvalues of an auxiliary one-dimensional operator with a curvature-induced potential.

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BibTeXRIS

Thomas Ourmières-Bonafos, Konstantin Pankrashkin. 2016-12-06. Discrete spectrum of interactions concentrated near conical surfaces. https://doi.org/10.1080/00036811.2017.1325472

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