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

摘要

The statistical properties of quantum transport through a chaotic cavity are encoded in the traces T_n,=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 T_n for all n. In particular, this provides the charge cumulants Q_ of all orders. We also compute the moments of the conductance g=T_1. All the results obtained are exact, i.e., they are valid for arbitrary numbers of open channels.