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DOI: 10.5445/IR/1000050414

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

Barseghyan, Diana; Exner, Pavel; Khrabustovskyi, Andrii; Tater, Miloš

We analyze two-dimensional Schrödinger operators with the potential jxyjp 􀀀 (x2 + y2)p=(p+2) where p 1 and 0, which exhibit an abrupt change of its spectral properties at a critical value of the coupling constant . We show that in the supercritical case the spectrum covers the whole real axis. In contrast, for below the critical value the spectrum is purely discrete and we establish a Lieb-Thirring-type bound on its moments. In the critical case the essential spectrum covers the positive hal ine while the negative spectrum can be only discrete, we demonstrate numerically the existence of a ground state eigenvalue.

Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2015
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-504145
KITopen-ID: 1000050414
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2015/6
Schlagworte Schrödinger operator, eigenvalue estimates, spectral transition
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