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}
}
  • Diana Barseghyan, P. Exner, +1 author M. Tater
  • Published 2015
  • Mathematics, Physics
  • arXiv: Mathematical Physics
  • 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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