Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

Details Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

1996-06-07

arxiv.org/abs/cond-mat/9606044v1

J. Math. Phys. 37 (1996) 5061

Physics

Condensed Matter

35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics

Scientific paper

10.1063/1.531676

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.

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