Quantum transport through ballistic cavities: Soft vs hard quantum chaos

We study transport through a two-dimensional billiard attached to two infin ite leads by numerically calculating the Landauer conductance and the Wigne r time delay. In the generic case of a mixed phase space we find a power-la w distribution of resonance widths and a power-law dependence of conductanc e increments apparently reflecting the classical dwell time exponent, in st riking difference to the case or a Fully chaotic phase space. Surprisingly, these power laws appear on energy scales below the mean level spacing, in contrast to semiclassical expectations.