Excess conductance of a spin-filtering quantum dot

The conductance G of a pair of single-channel point contacts in series, one of which is a spin filter, increases from 1/2 to 2/3 x e^2/h with more and more spin-flip scattering. This excess conductance was observed in a quantum dot by Zumbuhl et al., and proposed as a measure for the spin relaxation time T_1. Here we present a quantum mechanical theory for the effect in a chaotic quantum dot (mean level spacing Delta, dephasing time tau_phi, charging energy e^2/C), in order to answer the question whether T_1 can be determined independently of tau_phi and C. We find that this is possible in a time-reversal-symmetry-breaking magnetic field, when the average conductance follows closely the formula <G>=(2e^2/h)(T_1+h/Delta)/(4T_1+3h/Delta).