The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Journal of Spectral Theory


Full-Text PDF (240 KB) | Metadata | Table of Contents | JST summary
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