We describe a family of half-line continuum Schrödinger operators with purely singular continuous spectrum on , 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.
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Jonathan Breuer, Daniel Weissman, Level repulsion for Schrödinger operators with singular continuous spectrum. J. Spectr. Theory 9 (2019), no. 2, pp. 429–451DOI 10.4171/JST/252