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Spectral Statistics Beyond Random Matrix Theory

A. V. Andreev·B. L. Altshuler
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Abstract

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the Heisenberg time. We find that the singularities (present for random matrix ensembles) are washed out in a grain with a finite conductance. The results are nonuniversal (they depend on the shape of the grain and on its conductance), though they suggest a generalization for any system with finite Heisenberg time.

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A. V. Andreev, B. L. Altshuler. 1995-03-27. Spectral Statistics Beyond Random Matrix Theory. https://doi.org/10.1103/physrevlett.75.902

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