Universal level dynamics of complex systems

Pragya, Shukla (1999) Universal level dynamics of complex systems. In: Physical Review E, 59 (5). pp. 5205-5213.

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Abstract

We study the evolution of the distribution of eigenvalues of a N3N matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble and (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in case (i), a redefiniton of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invaraiant measure). This equivalence can therefore help us to obtain the correlations for various physically significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large N values, our results for both cases (i) and (ii) are similar to those obtained for the Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in the thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore the universality of dynamics of the eigenvalues of complex systems. [S1063-651X(99)04404-9] PACS number(s): 05.45.-a, 03.65.Sq, 05.40.-a

Item Type:	Journal Article
Publication:	Physical Review E
Publisher:	American Institute of Physics
Additional Information:	Copyright of this article belongs to American Institute of Physics.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	13 Sep 2006
Last Modified:	19 Sep 2010 04:30
URI:	http://eprints.iisc.ac.in/id/eprint/8194

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