Statistical Modeling of Wave Chaotic Transport and Tunneling
Ming‐Jer Lee · 2013
This thesis treats two general problem areas in the field of wave chaos. The first problem area that we address concerns short wavelength tunneling from a classically confined region in which the classical orbits are chaotic. We de-velop a quantitative theory for the statistics of energy level splittings for symmetric chaotic wells separated by a tunneling barrier. Our theory is based on the ran-dom plane wave hypothesis. While the fluctuation statistics are very different for chaotic and non-chaotic well dynamics, we show that the mean splittings of differ-ently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves. Our second problem area concerns the statistical properties of the impedance matrix (related to the scattering matrix) describing the input/output properties of waves in cavities in which ray trajectories that are regular and chaotic coexist (i.e., ‘mixed ’ systems). The impedance can be written as a summation over eigenmodes where the eigenmodes can typically be classified as either regular or chaotic. By