Statistical Properties of Transmission Spectra of Ergodic Wave Billiards: Random Hamiltonian Approach
Rozhkov, Igor Sergeevitch
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https://hdl.handle.net/2142/87717
Description
Title
Statistical Properties of Transmission Spectra of Ergodic Wave Billiards: Random Hamiltonian Approach
Author(s)
Rozhkov, Igor Sergeevitch
Issue Date
2003
Doctoral Committee Chair(s)
Weaver, Richard L.
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Acoustics
Language
eng
Abstract
Finally, we considered the experimental realization of the RMT system. We examined the dissipation of diffuse ultrasonic energy in a reverberant body coupled to a waveguide, i.e. in an open ergodic system. A simple model predicts a Porter-Thomas-like distribution of level widths and corresponding nonexponential dissipation, a behavior largely confirmed by measurements. For the case of fully open channels, however, measurements deviate from this model to a statistically significant degree. A supersymmetric calculation is found to model the observed behaviors accurately. In conclusion we discussed a possibility to find a more realistic 'naive' model that takes both the RMT and eigenmode complexity into account, but is less technically involved than the supersymmetry method. Such a modification of the naive approach is likely to be useful in studies of power variance and transient decay in chaotic cavities.
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