Integrable theory of quantum transport in chaotic cavities

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Osipov, Vladimir Al.
Kanzieper, Eugene
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Abstract
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The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.
Comment: 4 pages; final version to appear in Physical Review Letters
Keywords
Condensed Matter - Mesoscale and Nanoscale Physics, High Energy Physics - Theory, Mathematical Physics, Nonlinear Sciences - Chaotic Dynamics, Nonlinear Sciences - Exactly Solvable and Integrable Systems
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