Discrete spectrum of interactions concentrated near conical surfaces. Issue 9 (4th July 2018)

• Record Type: Journal Article
• Authors: Ourmières-Bonafos, Thomas; Pankrashkin, Konstantin
• Is Part Of: Applicable analysis. Volume 97:Issue 9(2018)
• Page Start: 1628
• Page End: 1649
• Publication Date: 2018-07-04
• Subjects: Schrödinger operator -- Dirichlet Laplacian -- conical surface -- eigenvalue; 35J05 -- 35P20 -- 35J20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1325472
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: We study the spectrum of two kinds of operators involving a conical geometry: the Dirichlet Laplacian in conical layers and Schrödinger operators with attractive -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.