Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces Tₙ=Tr[(tt^)ⁿ], where t is the transmission matrix. Within the random matrix theory approach, these traces are random variables whose probability distribution depends on the symmetries of the system. For the case of broken time-reversal symmetry, we use generalizations of Selberg's integral and the theory of symmetric polynomials to present explicit closed expressions for the average value, and for the variance of Tₙ for all n. In particular, this provides the charge cumulants ⟨⟨Qₙ⟩⟩ of all orders. We also compute the moments ⟨gⁿ⟩ of the conductance g=T₁. All the results obtained are exact, i.e., they are valid for arbitrary numbers of open channels.