Integrable theory of quantum transport in chaotic cavities
arXiv:0806.2784 · doi:10.1103/PhysRevLett.101.176804
Abstract
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 of propagating modes. Expressed in terms of solutions to the fifth Painlevé transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large- limit that reveals long exponential tails in the otherwise Gaussian curve.
4 pages; final version to appear in Physical Review Letters
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