TITLE:
Structure and Curvatures of Trajectories of a 2D Log-Gas
AUTHORS:
M. P. Pato, O. Bohigas
KEYWORDS:
Statistical Mechanics, Random Matrix Theory, Quantum Hall Effect
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.5,
April
24,
2014
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.