Topological Spectral Correlations in 2D Disordered Systems

TL;DR

This paper demonstrates that the tail behavior of the two-level spectral correlation function in 2D disordered systems is solely determined by the surface's topology, linking spectral properties to geometric characteristics.

Contribution

It establishes a direct relationship between spectral correlations and surface topology in 2D disordered systems, revealing topological influence on spectral statistics.

Findings

Spectral correlation tail depends on surface Euler characteristic.

The formula applies within specific conductance regimes.

Topology influences spectral correlations in 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: $R(s)=-\chi/(6\pi^2\beta s^2)$, where $\beta$ = 1,2 or 4 for the orthogonal, unitary and symplectic ensembles, and $\chi$ = 2(1-p) is the Euler characteristics of the surface with p "handles" (holes). The result is valid for g << s << g^2 for $\beta$=1,4 and for g << s << g^3 for $\beta$=2, where g >> 1 is the dimensionless conductance.