SEMICLASSICAL ANALYSIS OF THE BALLISTIC WEAK-LOCALIZATION IN CHAOTIC BILLIARDS - ROLE OF PARTIALLY TIME-REVERSED PAIRS OF PATHS

The ballistic weak-localization (WL) effect in chaotic billiards is st udied using an extended semiclassical approximation. We show that diff raction-induced partially time-reversed pairs of paths are essential t o describe the WL effect. By incorporating such pairs, we obtain the W L correction to both the transmission and reflection coefficients, whi ch satisfies the unitarity. This result provides an answer for the puz zle addressed by Baranger et al. [Phys. Rev. Lett. 70 (1993) 3876] tha t the WL correction arises only in the reflection coefficient but not in the transmission coefficient so long as the usual semiclassical app roximation is employed. We also find the full expression of the WL cor rection in the presence of a weak magnetic field.