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Journal of Spectral Theory


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Volume 9, Issue 2, 2019, pp. 429–451
DOI: 10.4171/JST/252

Published online: 2018-10-24

Level repulsion for Schrödinger operators with singular continuous spectrum

Jonathan Breuer[1] and Daniel Weissman[2]

(1) The Hebrew University of Jerusalem, Israel
(2) The Hebrew University of Jerusalem, Israel

We describe a family of half-line continuum Schrödinger operators with purely singular continuous spectrum on $(0, \infty)$, 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.

Keywords: Schrödinger operator, singular continuous spectrum, Christoffel–Darboux kernel, clock behavior

Breuer Jonathan, Weissman Daniel: Level repulsion for Schrödinger operators with singular continuous spectrum. J. Spectr. Theory 9 (2019), 429-451. doi: 10.4171/JST/252