Incollection,
Level and Eigenfunction Statistics of Disordered Systems: A common Mathematical Formulation
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
We present an analytical formulation for the statistics of energy levels
and eigenfunctions of disordered systems with/without e-e interactions, and, of arbitrary dimensions and boundary conditions. We find that the statistics behaves in a way similar to that of the single parametric Brownian ensembles. The latter appear during a Poisson to Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems at the metal-insulator transition as well as a tool to obtain them at the critical point for a wide range of disorders.
The formulation can also be extended to systems with e-e interaction
which helps us to reveal many important features of the statistics in
interacting systems e.g. a critical point behavior different from that of
non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level and eigenfunction correlations.
