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Diagrammatic Analysis of the Unitary Group for Double Barrier Ballistic Cavities: Equivalence with Circuit Theory

Anderson L. R. Barbosa·Antonio M. S. Macedo
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Abstract

We derive a set of coupled non-linear algebraic equations for the asymptotics of the Poisson kernel distribution describing the statistical properties of a two-terminal double-barrier chaotic billiard (or ballistic quantum dot). The equations are calculated from a diagrammatic technique for performing averages over the unitary group, proposed by Brouwer and Beenakker [J. Math. Phys. 37, 4904 (1996)]. We give strong analytical evidences that these equations are equivalent to a much simpler polynomial equation calculated from a recent extension of Nazarov's circuit theory [A. M. S. Macedo, Phys. Rev. B 66, 033306 (2002)]. These results offer interesting perspectives for further developments in the field via the direct conversion of one approach into the other.

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Anderson L. R. Barbosa, Antonio M. S. Macedo. 2005-04-04. Diagrammatic Analysis of the Unitary Group for Double Barrier Ballistic Cavities: Equivalence with Circuit Theory. https://doi.org/10.1103/physrevb.71.235307

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