We use a semiclassical approximation to study the transport through the weakly open chaotic Sinai quantum billiards which can be considered as the schematic of a Sinai mesoscopic device,with the diffractive scatterings at the lead openings taken into account.The conductance of the ballistic microstructure which displays universal fluctuations due to quantum interference of electrons can be calculated by Landauer formula as a function of the electron Fermi wave number,and the transmission amplitude can be expressed as the sum over all classical paths connecting the entrance and the exit leads.For the Sinai billiards,the path sum leads to an excellent numerical agreement between the peak positions of power spectrum of the transmission amplitude and the corresponding lengths of the classical trajectories,which demonstrates a good agreement between the quantum theory and the semiclassical theory.
Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.
