Mesoscopic junctions, random scattering, and strange repellers

Ballistic transport through a two-dimensional cross junction is chaotic. The classical transmissivity, from which total transmission coefficients are obtained, exhibits self-similar regions of high transparency about a hierarchy of injection angles, ${\mathrm{\alpha }}_{\mathit{N}}$. These geometrical channels dominate the phase space of possible exits from the junction. Long dwell times within the junction, a manifestation of irregular scattering, strongly enhance the role of random processes in real devices.