Y. Takane et K. Nakamura, SEMICLASSICAL ANALYSIS OF THE BALLISTIC WEAK-LOCALIZATION IN CHAOTIC BILLIARDS - ROLE OF PARTIALLY TIME-REVERSED PAIRS OF PATHS, Journal of the Physical Society of Japan, 66(10), 1997, pp. 2977-2980
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.