Semiclassical scattering in a circular semiconductor microstructure

The conductance of a microscopic junction shows fluctuations caused by quantum interference of waves that follow different paths between the leads. We give a semiclassical formula for these fluctuations. The theory utilizes trajectories which travel between the centers of the lead apertures; it also incorporates diffraction at these apertures. We extend the theory to include ''ghost paths,'' which scatter diffractively off the lead mouths. Semiclassical S-matrix elements are computed for a circular junction over a range of Fermi wave numbers, and the large-scale structure of these matric elements shows good agreement with quantum results. Finally, we propose a hypothesis about the effect of the quantum coherence length on the S matrix and on the semiclassical sum.