Geometry-dependent scattering through Ballistic microstructures: Semiclassical theory beyond the stationary-phase approximation

The conductance of a ballistic microstructure shows strong fluctuations as a function of the Fermi wave number. We present a semiclassical theory that describes these fluctuations in terms of bundles of short trajectories. These trajectories provide the dominant contribution to electron transport through a weakly open microstructure. For the coupling between the quantum wires and the cavity, contributions beyond the stationary phase approximation are taken into account giving rise to diffraction effects. A comparison with full quantum calculations for a rectangular billiard is made. The peak positions of the power spectrum agree very well between the quantum and semiclassical theories. Numerical evidence is found for the breakdown of the semiclassical approximation for long paths. A simple explanation in terms of the dispersion of the semiclassical wave packet in the interior of the cavity is proposed.