0428327 - ÚJF 2015 RIV JP eng J - Journal Article
Kondej, S. - Krejčiřík, David
Spectral Analysis of a Quantum System with a Double Line Singular Interaction.
Publications of the Research Institute for Mathematical Sciences. Roč. 49, č. 4 (2013), s. 831-859. ISSN 0034-5318. E-ISSN 1663-4926
R&D Projects: GA ČR GAP203/11/0701
Institutional support: RVO:61389005
Keywords : Schrödinger operator * singular perturbation * spectral analysis * Hardy inequality * resonance
Subject RIV: BE - Theoretical Physics
Impact factor: 0.614, year: 2013

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically approaches a constant value, and find conditions which guarantee either the existence of discrete eigenvalues or Hardy-type inequalities. For a class of our models admitting mirror symmetry, we also establish the existence of embedded eigenvalues and show that they turn into resonances after introducing a small perturbation.
Permanent Link: http://hdl.handle.net/11104/0233680