Level and Eigenfunction Statistics of Disordered Systems: A common Mathematical Formulation
P. Shukla. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Zusammenfassung
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.
%0 Book Section
%1 statphys23_0025
%A Shukla, P.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K gaussian matrix random statphys23 topic-1
%T Level and Eigenfunction Statistics of Disordered Systems: A common Mathematical Formulation
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=25
%X 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.
@incollection{statphys23_0025,
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.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Shukla, P.},
biburl = {https://www.bibsonomy.org/bibtex/224f3a3f55a4c21ac95a6c724d7a51b0a/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {e4e0450c39a4f6eb2c6a22d4a1e5cf2e},
intrahash = {24f3a3f55a4c21ac95a6c724d7a51b0a},
keywords = {gaussian matrix random statphys23 topic-1},
month = {9-13 July},
timestamp = {2007-06-20T10:16:09.000+0200},
title = {Level and Eigenfunction Statistics of Disordered Systems: A common Mathematical Formulation},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=25},
year = 2007
}