J. Phys. I France
Volume 6, Numéro 4, April 1996
Page(s) 455 - 468
DOI: 10.1051/jp1:1996224
J. Phys. I France 6 (1996) 455-468

Periodic and Non-Periodic Band Random Matrices: Structure of Eigenstates

Felix M. Izrailev1, 2, Luca Molinari3 and Karol Zyczkowski4

1  Universitá di Milano, sede di Como, via Lucini 3, 22100 Como, Italy
2  Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
3  Dipartimento di Fisica and INFN, Via Celoria 16, 20133 Milano, Italy
4  Uniwersytet Jagiellonski, Instytut Fizyki M. Smoluchowskiego, ul. Reymonta 4, 30-059 Kraków, Poland

(Received 5 October 1995, accepted 5 January 1996)

The structure of eigenstates for the ensembles of standard and periodic Band Random Matrices (BRM) is analysed. The main attention is drawn to the scaling properties of the inverse participation ratio and other measures of localization length. Numerical data are compared with analytical results recently derived for standard BRMs of very large band size. The data for periodic and standard BRM allow us to exhibit the influence of boundary conditions on the properties of eigenstates.

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