Chaos in two-dimensional electron waveguides

We show that the S-matrix for electrons propagating in a waveguide has different statistical properties depending on whether the waveguide cavity shape gives rise to chaotic or integrable behavior classically. Although our direct numerical calculation of the electron wave function is convenient to do accurate calculation about microscopic details on the system it is not efficient to produce accurate statistics. A modified version of reaction matrix theory has been introduced. Statistical properties of Wigner delay times and the effect of evanescent modes on the deterministic scattering of an electron matter wave from a classically chaotic 2-d electron waveguide is studied for the case of 2, 6, and 16 propagating modes. Deterministic reaction matrix theory for this system is generalized to include the effect of evanescent modes on the scattering process. The statistical properties of the Wigner delay times for the deterministic scattering process are compared to the predictions of random reaction matrix theory.