Statistics of conductance and shot-noise power for chaotic cavities

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We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$.

• With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly.
• We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges.
• For $0<g<1$ a power law for the conductance distribution is exact.