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Spectral statistics in disordered metals: a trajectories approach

Robert A. Smith·Igor V. Lerner·Boris L. Altshuler
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Abstract

We show that the perturbative expansion of the two-level correlation function, $R(ω)$, in disordered conductors can be understood semiclassically in terms of self-intersecting particle trajectories. This requires the extension of the standard diagonal approximation to include pairs of paths which are non-identical but have almost identical action. The number of diagrams thus produced is much smaller than in a standard field-theoretical approach. We show that such a simplification occurs because $R(ω)$ has a natural representation as the second derivative of free energy $F(ω)$. We calculate $R(ω)$ to 3-loop order, and verify a one-parameter scaling hypothesis for it in 2d. We discuss the possibility of applying our ``weak diagonal approximation'' to generic chaotic systems.

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Robert A. Smith, Igor V. Lerner, Boris L. Altshuler. 1998-01-22. Spectral statistics in disordered metals: a trajectories approach. https://doi.org/10.1103/physrevb.58.10343

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