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

@article{Barseghyan2015SpectralAO, title={Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition}, author={Diana Barseghyan and P. Exner and A. Khrabustovskyi and M. Tater}, journal={arXiv: Mathematical Physics}, year={2015} }

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… CONTINUE READING

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