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oai:drum.lib.umd.edu:1903/145242016-03-29T10:57:52Zcom_1903_2269com_1903_12com_1903_2col_1903_2800col_1903_3

Ott, Edward Lee, Ming-Jer Digital Repository at the University of Maryland University of Maryland (College Park, Md.) Physics 2013-10-04T05:30:55Z 2013-10-04T05:30:55Z 2013 http://hdl.handle.net/1903/14524 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 appropriate characterizations of regular and chaotic contributions, we obtain statis- tical predictions for the impedance. We then test these predictions by comparison with numerical calculations for a specific cavity shape, obtaining good agreement. Statistical Modeling of Wave Chaotic Transport and Tunneling Dissertation Physics open.access