JournalsjstVol. 9, No. 2pp. 429–451

Level repulsion for Schrödinger operators with singular continuous spectrum

  • Jonathan Breuer

    The Hebrew University of Jerusalem, Israel
  • Daniel Weissman

    The Hebrew University of Jerusalem, Israel
Level repulsion for Schrödinger operators with singular continuous spectrum cover

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Abstract

We describe a family of half-line continuum Schrödinger operators with purely singular continuous spectrum on (0,)(0, \infty), exhibiting asymptotic strong level repulsion (known as clock behavior). This follows from the convergence of the renormalized continuum Christoffel–Darboux kernel to the sine kernel.

Cite this article

Jonathan Breuer, Daniel Weissman, Level repulsion for Schrödinger operators with singular continuous spectrum. J. Spectr. Theory 9 (2018), no. 2, pp. 429–451

DOI 10.4171/JST/252