-In pseudo integrable systems diffractive scattering caused by wedges and impurities can be described within the framework of Geometric Theory of Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory of Diffraction (POTD). We derive formulas expressing the reflection and transition matrix elements for one and many diffractive points and apply it for impurity and wedge diffraction. Diffraction can cause backscattering in situations, where usual semiclassical backscattering is absent causing an erodation of ideal conductance steps. The length of diffractive periodic orbits and diffractive loops can be detected in the power spectrum of the reflection matrix elements.The tail of the power spectrum shows ∼ 1/l 1/2 decay due to impurity scattering and ∼ 1/l 3/2 decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.In recent years, semiclassical methods became very popular in describing devices operating in the mesoscopic regime. There are two entirely different sets of theoretical tools which have been used in a wide range of applications. One of them is a WKB based short wavelength description [1, 2] where classical trajectories, chaos, regularity and analytic properties of the potential play a major role. The other is based on random matrix models or on averaging over random Gaussian potentials [3]. The first approach is designed to describe clean systems where the potential depends smoothly on coordinates and parameters, while the second assumes a system densely packed with impurities causing wild fluctuations of the potential on all length scales.Fortunately, advances in manufacturing and material design reduced the average number of impurities exponentially since the eighties and this trend is expected to continue in the future. Accordingly, a realistic semiclassical theory should be capable to treat systems with low number of impurities and not only completely clean or completely dirty ones. Another demand is that human designed structures,
The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-Büttiker formula. In the case of few impurities the conductance is proportional to the number of the open channels N of the empty waveguide and shows a regular staircase like behavior with step heights ≈ 2e 2 /h. For large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands (smaller than N ) times the universal constant 2e 2 /h. This lower value is reached exponentially with increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum-chaotic. The conductance, in units of 2e 2 /h, changes from N corresponding to the empty waveguide to ∼ N/2 corresponding to chaotic or disordered system. It turnes out, that the conductance can be expressed as (1 − c/2)N where the parameter 0 < c < 1 measures the chaoticity
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