Interplay of Ehrenfest and Dephasing Times in Ballistic Conductors

Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this Letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.

Figure 1

Schematic drawing of a Lorentz gas and a generic pair of trajectories ${\alpha }_1$ (solid line) and ${\alpha }_2$ (dotted line) that contributes to the ensemble average $⟨\delta G⟩$ of the quantum interference correction to the conductance.

Figure 2

Semiclassical representation of the two distinct contributions to the conductance fluctuations [(a), (b)]. Figure (c) shows a detail of one pair of trajectories shown in panel (b) for the case that the Ehrenfest time is comparable to the period of the center periodic orbit. The multiplicity of the winding around one center periodic orbit implies a number of exceptional features, as discussed in the text below Eq. (3).