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19 April 2024
 
  » arxiv » cond-mat/9801229

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Spectral statistics in disordered metals: a trajectories approach
Robert A. Smith ; Igor V. Lerner ; Boris L. Altshuler ;
Date 22 Dec 1997
Journal Phys. Rev. B 58 (1998) 10343
Subject Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall
AffiliationBirmingham), Igor V. Lerner (Birmingham), Boris L. Altshuler (Princeton
AbstractWe 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.
Source arXiv, cond-mat/9801229
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