We study quantum transport through ballistic cavities coupled to two electron reservoirs by point contacts. We develop a powerful method, based on supersymmetry, to calculate exactly transmission eigenvalue statistics in the presence of tunnel barriers and for a small number of open scattering channels. We calculate the transmission eigenvalue density for ballistic point contacts and find it to be consistent with a distribution of transmission eigenvalues given by the Jacobi ensemble from random-matrix theory. We also calculate explicitly the transmission eigenvalue density for quantum dots with tunneling point contacts.

• Received 30 June 1998

DOI:https://doi.org/10.1103/PhysRevB.58.R13379