Transmission Eigenvalue Densities and Moments in Chaotic Cavities from Random Matrix Theory

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Vivo, Pierpaolo
Vivo, Edoardo
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Abstract
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We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble of Random Matrix Theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form $<\lambda_1^m>$ for $m>-|N_1-N_2|-1$ and $\beta=2$, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation functions for $\beta=2,4$ which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants.
Comment: Slight extension of the published version. One reference added; main result (16) simplified
Keywords
Condensed Matter - Mesoscale and Nanoscale Physics, Condensed Matter - Statistical Mechanics
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