Level repulsion for Schroedinger operators with singular continuous spectrum

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.

References in corpus (2)

• The Canopy Graph and Level Statistics for Random Operators on Trees
• Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum