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Statistics of quantum transport in weakly non-ideal chaotic cavities

We consider statistics of electronic transport in chaotic cavities where time-reversal symmetry is broken and one of the leads is weakly non-ideal, i.e. it contains tunnel barriers characterized by tunneling probabilities $Γ_i$. Using symmetric function expansions and a generalized Selberg integral, we develop a systematic perturbation theory in $1-Γ_i$ valid for arbitrary number of channels, and obtain explicit formulas up to second order for the average and variance of the conductance, and for the average shot-noise. Higher moments of the conductance are considered to leading order.