Ehrenfest Time and the Coherent Backscattering Off Ballistic Cavities

If the Ehrenfest time ${\tau }_{\mathrm{E}}$ of a ballistic cavity is not negligible in comparison to its dwell time ${\tau }_{\mathrm{D}}$, the weak localization correction to the cavity’s transmission is suppressed proportional to $\exp (-{\tau }_{\mathrm{E}}/{\tau }_{\mathrm{D}})$. At the same time, quantum interference enhances the probability of reflection into the mode of incidence by a factor two. This “enhanced backscattering” does not depend on the Ehrenfest time. We show that, in addition to the diagonal enhanced backscattering, there are off-diagonal contributions to coherent backscattering that become relevant if ${\tau }_{\mathrm{E}}\gtrsim {\tau }_{\mathrm{D}}$.

Figure 1

Schematic drawing of pairs of classical trajectories contribution to coherent backscattering (a) and (b) and weak localization (c).

Figure 2

Left: the surface of section of a band, together with the definitions of the band’s center momentum, momentum range $r$, and momentum width $w$. The maximal transverse momentum is the Fermi momentum $p_F$. Right: a band and its image. The image band is the surface of section of the trajectories in the band upon exit, with the transverse momentum $p_{\perp }$ reversed.