On the spectrum of narrow Neumann waveguide with periodically distributed traps. (15th July 2015)

• Record Type: Journal Article
• Authors: Exner, Pavel; Khrabustovskyi, Andrii
• Is Part Of: Journal of physics. Volume 48:Number 31(2015)
• Publication Date: 2015-07-15
• Subjects: periodic waveguides -- Schrödinger operators -- interaction -- spectrum -- gaps -- asymptotic analysis; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/31/315301
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We analyze a family of singular Schrödinger operators describing a Neumann waveguide with a periodic array of singular traps of a type. We show that in the limit when perpendicular size of the guide tends to zero and the interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.