Dependence of critical level statistics on the sample shape

The level-spacing distribution of consecutive energy eigenvalues is calculated numerically at the metal insulator transition for 3d systems with different cuboid shapes. It is found that the scale independent critical \(P_c(s)\) changes as a function of the aspect ratio of the samples while the crit...

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Bibliographic Details
Published inarXiv.org
Main Authors Potempa, H, Schweitzer, L
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.04.1998
Subjects
Aspect ratio
Critical point
Dependence
Eigenvalues
Energy distribution
Mathematical analysis
Resistance
Statistical methods
Statistics
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Summary:The level-spacing distribution of consecutive energy eigenvalues is calculated numerically at the metal insulator transition for 3d systems with different cuboid shapes. It is found that the scale independent critical \(P_c(s)\) changes as a function of the aspect ratio of the samples while the critical disorder \(W_c/V=16.4\) remains the same. We use our data to test whether an expression for the small-\(s\) behaviour of the level statistics proposed by Kravtsov and Mirlin for the metallic regime is applicable also at the critical point. For this reason, a shape dependent dimensionless critical conductance \(g_c\) has been extracted from the small-\(s\) behaviour of the critical level statistics. Our result for a cubic sample, \(g_c=0.112\pm 0.005\), is in good agreement with a value obtained previously from calculations using the Kubo-formula.
ISSN:2331-8422
DOI:10.48550/arxiv.9804312