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

DOI: 10.4236/jamp.2014.25005, PP. 32-38

Keywords: Statistical Mechanics, Random Matrix Theory, Quantum Hall Effect

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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.

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