Topological Spectral Correlations in 2D Disordered Systems

Abstract

It is shown that the tail in the two-level spectral correlation function R(s) for particles on 2D closed disordered surfaces is determined entirely by surface topology: $R(s)=-χ/(6π^2βs^2)$, where $β$ = 1,2 or 4 for the orthogonal, unitary and symplectic ensembles, and $χ$ = 2(1-p) is the Euler characteristics of the surface with p &#34;handles&#34; (holes). The result is valid for g << s << g^2 for $β$=1,4 and for g << s << g^3 for $β$=2, where g >> 1 is the dimensionless conductance.