Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition

0458929 - ÚJF 2017 RIV GB eng J - Journal Article
Barseghyan, Diana - Exner, Pavel - Khrabustovskyi, A. - Tater, Miloš
Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition.
Journal of Physics A-Mathematical and Theoretical. Roč. 49, č. 16 (2016), s. 165302. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : Schrodinger operator * eigenvalue estimates * spectral transition
Subject RIV: BE - Theoretical Physics
Impact factor: 1.865, year: 2016

We analyze two-dimensional Schrodinger operators with the potential vertical bar xy vertical bar(p)-lambda(x(2)+ y(2))(p/(p+2)) where p >= 1 and lambda >= 0 which exhibit an abrupt change of spectral properties at a critical value of the coupling constant lambda. We show that in the supercritical case the spectrum covers the whole real axis. In contrast, for lambda below the critical value the spectrum is purely discrete and we establish a Lieb-Thirring-type bound on its moments. In the critical case where the essential spectrum covers the positive halfline while the negative spectrum can only be discrete, we demonstrate numerically the existence of a ground-state eigenvalue.
Permanent Link: http://hdl.handle.net/11104/0259139