Structure and Curvatures of Trajectories of a 2D Log-Gas

M. P. Pato^1*, O. Bohigas²

¹Instituto de Física, Universidade de S?o Paulo Caixa Postal, Sao Paulo, S.P., Brazil.
²CNRS, Université Paris-Sud, UMR8626, LPTMS, Orsay Cedex, France.

DOI: 10.4236/jamp.2014.25005                

Abstract

A model is constructed to study the statistical properties of irregular trajectories of a log-gas whose positions are those of the complex eigenvalues of the unitary Ginibre ensemble. It is shown that statistically the trajectories form a structure that reveals the eigenvalue departure positions. It is also shown that the curvatures of the ensemble of trajectories are Cauchy distributed.

Keywords

Statistical Mechanics, Random Matrix Theory, Quantum Hall Effect

Conflicts of Interest

The authors declare no conflicts of interest.

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