15-103 Diana Barseghyan, Pavel Exner, Andrii Khrabustovskyi, Milos Tater
Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition (611K, pdf) Oct 31, 15
Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. We analyze two-dimensional Schr\"odinger operators with the potential $|xy|^p - \lambda (x^2+y^2)^{p/(p+2)}$ where $p\ge 1$ and $\lambda\ge 0$, which exhibit an abrupt change of its 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 the essential spectrum covers the positive halfline while the negative spectrum can be only discrete, we demonstrate numerically the existence of a ground state eigenvalue.

Files: 15-103.src( 15-103.keywords , transition151030.pdf.mm )