Gap asymptotics in a weakly bent leaky quantum wire

0454109 - ÚJF 2016 RIV GB eng J - Journal Article
Exner, Pavel - Kondej, S.
Gap asymptotics in a weakly bent leaky quantum wire.
Journal of Physics A-Mathematical and Theoretical. Roč. 48, č. 49 (2015), s. 495301. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : singular Schroedinger operators * delta interaction * leaky quantum wires * weak perturbation * asymptotic expansion
Subject RIV: BE - Theoretical Physics
Impact factor: 1.933, year: 2015

The main question studied in this paper concerns the weak-coupling behavior of the geometrically induced bound states of singular Schrodinger operators with an attractive delta interaction supported by a planar, asymptotically straight curve Gamma. We demonstrate that if Gamma is only slightly bent or weakly deformed, then there is a single eigenvalue and the gap between it and the continuum threshold is in the leading order proportional to the fourth power of the bending angle, or the deformation parameter. For comparison, we analyze the behavior of a general geometrical induced eigenvalue in the situation when one of the curve asymptotes is wiggled.
Permanent Link: http://hdl.handle.net/11104/0254805