Diffraction in the semiclassical description of mesoscopic devices

Abstract

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 $\sim 1/l^{1/2}$ decay due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering. We think this is a universal sign of the presence of diffractive scattering in pseudo integrable waveguides.

18 pages, Latex , eps

References in corpus (5)

• Periodic Orbit Theory of Diffraction
• The Role of Diffraction in the Quantization of Dispersing Billiards
• Diffractive orbits in quantum billiards
• Application of the diffraction trace formula to the three disk scattering system
• Semiclassical Quantisation Using Diffractive Orbits

Cited by in corpus (4)

• Pseudo-Path Semiclassical Approximation to Transport through Open Quantum Billiards: Dyson Equation for Diffractive Scattering
• Crossover from Regular to Chaotic Behavior in the Conductance of Periodic Quantum Chains
• Negative length orbits in normal-superconductor billiard systems
• Spectral Determinant Method for Interacting N-body Systems Including Impurities