Level repulsion for Schroedinger operators with singular continuous spectrum

2016/12/04 by Jonathan Breuer, Breuer, Jonathan, Daniel Weissman +2
Computer Science · Mathematics · #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.1612.01123

openalex publication_date 2016/12/04 · arxiv created 2017/08/26 · arxiv updated 2017/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a family of half-line continuum Schroedinger operators with purely singular continuous essential spectrum, 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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