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Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition
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SYSNO ASEP 0458929 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition Author(s) Barseghyan, Diana (UJF-V) ORCID, SAI
Exner, Pavel (UJF-V) RID, ORCID, SAI
Khrabustovskyi, A. (DE)
Tater, Miloš (UJF-V) RID, ORCID, SAINumber of authors 4 Source Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 49, č. 16 (2016), s. 165302Number of pages 19 s. Publication form Print - P Language eng - English Country GB - United Kingdom Keywords Schrodinger operator ; eigenvalue estimates ; spectral transition Subject RIV BE - Theoretical Physics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000372195600014 EID SCOPUS 84961589884 DOI 10.1088/1751-8113/49/16/165302 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2017
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