Time-Reversal Symmetry Breaking in Quantum Billiards.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2009)
Florian Schäfer - Dissertation - Time-Reversal Symmetry Breaking in Quantum Billiards -
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|Item Type:||Ph.D. Thesis|
|Title:||Time-Reversal Symmetry Breaking in Quantum Billiards|
The present doctoral thesis describes experimentally measured properties of the resonance spectra of flat microwave billiards with partially broken timereversal invariance induced by an embedded magnetized ferrite. A vector network analyzer determines the complex scattering matrix elements. The data is interpreted in terms of the scattering formalism developed in nuclear physics. At low excitation frequencies the scattering matrix displays isolated resonances. At these the effect of the ferrite on isolated resonances (singlets) and pairs of nearly degenerate resonances (doublets) is investigated. The hallmark of time-reversal symmetry breaking is the violation of reciprocity, i.e. of the symmetry of the scattering matrix. One finds that reciprocity holds in singlets; it is violated in doublets. This is modeled by an effective Hamiltonian of the resonator. A comparison of the model to the data yields time-reversal symmetry breaking matrix elements in the order of the level spacing. Their dependence on the magnetization of the ferrite is understood in terms of its magnetic properties. At higher excitation frequencies the resonances overlap and the scattering matrix elements fluctuate irregularly (Ericson fluctuations). They are analyzed in terms of correlation functions. The data are compared to three models based on random matrix theory. The model by Verbaarschot, Weidenmüller and Zirnbauer describes time-reversal invariant scattering processes. The one by Fyodorov, Savin and Sommers achieves the same for systems with complete time-reversal symmetry breaking. An extended model has been developed that accounts for partial breaking of time-reversal invariance. This extended model is in general agreement with the data, while the applicability of the other two models is limited. The cross-correlation function between forward and backward reactions determines the time-reversal symmetry breaking matrix elements of the Hamiltonian to up to 0.3 mean level spacings. Finally the sensitivity of the elastic enhancement factor to time-reversal symmetry breaking is studied. Based on the data elastic enhancement factors below 2 are found which is consistent with breaking of time-reversal invariance in the regime of overlapping resonances. The present work provides the framework to probe for broken time-reversal invariance in any scattering data by a multitude of methods in the whole range between isolated and overlapping resonances.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||Quantum chaos; Time-reversal invariance; Scattering; Fluctuations|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 530 Physik|
|Divisions:||05 Department of Physics > Institute of Nuclear Physics|
|Date Deposited:||05 Mar 2009 14:29|
|Last Modified:||07 Dec 2012 11:55|
|Referees:||Richter, Prof. Dr. Achim and Wambach, Prof. Dr. Jochen|
|Refereed:||26 January 2009|