SPECTRAL STATISTICS IN DISORDERED METALS - A TRAJECTORIES APPROACH

We show that the perturbative expansion of the two-level correlation f unction, R(omega), in disordered conductors can be understood semiclas sically in terms of self-intersecring particle trajectories. This requ ires the extension of the standard diagonal approximation to include p airs of paths that are nonidentical but have almost identical action. The number of diagrams thus produced is much smaller than in a standar d field-theoretical approach. We show that such a simplification occur s because R(omega) has a natural representation as the second derivati ve of free energy F(omega). We calculate R(omega) to three-loop order, and verify a one-parameter scaling hypothesis for it in two dimension s. We discuss the possibility of applying our ''weak diagonal approxim ation'' to generic chaotic systems. [S0163-1829(98)01736-5].