Ehrenfest time dependence of quantum transport corrections and spectral statistics

The Ehrenfest time scale in quantum transport separates essentially classical propagation from wave interference and here we consider its effect on the transmission and reflection through quantum dots. In particular we calculate the Ehrenfest time dependence of the next-to-leading-order quantum corrections to the transmission and reflection for dc and ac transport and check that our results are consistent with current conservation relations. Looking as well at closed systems, we finally demonstrate how the contributions analyzed here imply changes in the calculation given in [P. W. Brouwer, S. Rahav and C. Tian, Phys. Rev. E, 74, 066208 (2006)] of the next to leading order of the spectral form factor. Our semiclassical result coincides with the result obtained in [C. Tian and A. I. Larkin, Phys. Rev. B, 70, 035305 (2004)] by field-theoretical methods.