On the existence of bound states in asymmetric leaky wires

0458648 - ÚJF 2017 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: quantum wave-guides * graphs
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.077, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0258894