Size effect of diagonal random matrices
Joint Authors
Abu al-Majd, A. A.
Abu al-Majd, A. Y.
Source
Issue
Vol. 1, Issue 1 (30 Sep. 2011)12 p.
Publisher
Amgad Society for Developing the Community and Protecting the Environment
Publication Date
2011-09-30
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution.
In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems.
We evaluate the corresponding nearest-neighbor spacing (NNS) distribution, which characterizes the short range correlation between levels.
To characterize the long term correlations, we evaluate the level number variance.
We show that, by increasing the size of matrices, the level spacing distribution evolves from the Gaussian shape that characterizes ensembles of 2×2 matrices tending to the Poissonian as N → ∞.
The transition occurs at N ≈ 20.
The number variance also shows a gradual transition towards the straight line behavior predicted by the Poisson statistics.
American Psychological Association (APA)
Abu al-Majd, A. A.& Abu al-Majd, A. Y.. 2011. Size effect of diagonal random matrices. Alexandria Journal of Physics،Vol. 1, no. 1.
https://search.emarefa.net/detail/BIM-786589
Modern Language Association (MLA)
Abu al-Majd, A. A.& Abu al-Majd, A. Y.. Size effect of diagonal random matrices. Alexandria Journal of Physics Vol. 1, no. 1 (Sep. 2011).
https://search.emarefa.net/detail/BIM-786589
American Medical Association (AMA)
Abu al-Majd, A. A.& Abu al-Majd, A. Y.. Size effect of diagonal random matrices. Alexandria Journal of Physics. 2011. Vol. 1, no. 1.
https://search.emarefa.net/detail/BIM-786589
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-786589