  We investigate the effect of spatial symmetries on phase coherent electronic
transport through chaotic quantum dots. For systems which have a spatial
symmetry that interchanges the source and drain leads, we find in the framework
of random matrix theory that the density of the transmission eigenvalues is
indepedent of the number of channels N in the leads. As a consequence, the weak
localization correction to the conductance vanishes in these systems, and the
shot noise suppression factor F is independent of N. We confirm this prediction
by means of numerical calculations for stadium billiards with various lead
geometries. These calculations also uncover transport signatures of partially
preserved symmetries.

Mesoscale and Nanoscale Physics