On the existence of bound states in asymmetric leaky wires

0458648 - ÚJF 2017 RIV US eng J - Journal Article
Exner, Pavel - Vugalter, S.
On the existence of bound states in asymmetric leaky wires.
Journal of Mathematical Physics. Roč. 57, č. 2 (2016), s. 022104. ISSN 0022-2488. E-ISSN 1089-7658
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : quantum wave-guides * graphs
Subject RIV: BE - Theoretical Physics
Impact factor: 1.077, year: 2016

We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive delta-interaction supported by a non-straight, piecewise smooth curve L dividing the plane into two regions of which one, the "interior," is convex. The other interaction component is a constant positive potential V-0 in one of the regions. We show that in the critical case, V-0 = alpha(2), the discrete spectrum is non-void if and only if the bias is supported in the interior. We also analyze the non-critical situations, in particular, we show that in the subcritical case, V-0 < alpha(2), the system may have any finite number of bound states provided the angle between the asymptotes of L is small enough.
Permanent Link: http://hdl.handle.net/11104/0258894