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

2016 
We analyze two-dimensional Schrodinger operators with the potential where and which exhibit an abrupt change of spectral properties at a critical value of the coupling constant λ. We show that in the supercritical case the spectrum covers the whole real axis. In contrast, for λ 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.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    21
    References
    8
    Citations
    NaN
    KQI
    []