Topological Spectral Correlations in 2D Disordered Systems

Details Topological Spectral Correlations in 2D Disordered Systems Topological Spectral Correlations in 2D Disordered Systems

1998-09-17

arxiv.org/abs/cond-mat/9809235v1

Phys. Rev. Lett. v.82, 157 (1999)

Physics

Condensed Matter

4 pages, revtex

Scientific paper

10.1103/PhysRevLett.82.157

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.

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