Quantum-mechanical propagation of electrons through a kink and the Anderson-localization problem

The localization characteristics of quantum-mechanical propagation of electrons through a disordered mesoscopic system are emulated in the simple geometry of a rectangular kink. The Landauer-Buttiker prescription and transfer-matrix method are combined in solving the corresponding Anderson-localization problem. The strong localization, which characterizes a one-dimensional system, the weak localization in a two-dimensional system, and universal conductance fluctuations are found to be compatible with the predictions of single-parameter scaling theory. Conductance fluctuations are also found in the emulation of conductance in the ballistic regime. These chaotic fluctuations are interpreted as a complex spectrum of resonating electron waves within a waveguide. The statistical distribution of fluctuations due to different realizations of the disorder in systems of identical macroscopic characteristics is also investigated. The significant deviations from a normal Gaussian distribution implied by the one-parameter scaling theory indicate the inadequacy of that theory and the need for higher-order corrections.