(untitled) (Journal of Atomic and Molecular Sciences, 2015)
We study the transport through weakly open rectangular billiards by a new semiclassical approach within the framework of the Fraunhofer diffraction. Based on a Dyson equation for the semiclassical Green's function, the transmission amplitude can be expressed as the sum over all classical trajectories connecting the entrance and the exit leads. We find that the peak positions of the transmission power spectrum not only correspond to classical trajectories but associate with a lot of nonclassical trajectories and the contributions to the power spectrum of the transmission amplitude for the first mode are largely depending on the classical trajectories with small incident angles showing a good agreement with the diffracted angular distribution within the framework of the diffractive scattering effect at the lead openings.