Spectral statistics in disordered metals: a trajectories approach

Abstract

We show that the perturbative expansion of the two-level correlation function, $R(\omega )$, 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 $R(\omega )$ has a natural representation as the second derivative of free energy $F(\omega )$. We calculate $R(\omega )$ 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.

9 pages in REVTeX two-column format including 4 figures; submitted to Phys.Rev.B

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