Level repulsion for Schroedinger operators with singular continuous   spectrum
  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. 
Jonathan Breuer, Daniel Weissman
math.SP