Semiclassical Calculation of Conductance Transmission through an Open Equilateral Triangular Billiards

We study the transport property passing through a weakly open equilateral triangular billiards by using the semiclassical method. We extend the Green function and the transport matrix theory to include the multiple scattering effect at the boundary and the diffractions of the pair of the lead apertures. For analysing the structure of semiclassical pseudo path kinks, the geometric and the special dynamical symmetries of the system are simultaneously taken into account. The conductance is calculated by Landauer formula as a function of the electron's Fermi wave number. Its Fourier transformation, the quantum path-length spectrum, is qualitatively in accordance with the results of the classical trajectories, which indicates that such approach provides an obvious improvement of the semiclassical description. (general)