Statistics of Conductance and Shot-Noise Power for Chaotic Cavities

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$\text{}_{1,2}$ of channels in two leads and symmetry parameterβ = 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. All results are also consistent with numerical simulations.