Available Projects for Bachelor- and Master-Theses

The following list comprises possible subjects for Bachelor- and Master-theses in the Quantum Chaos Group. Other subjects are also available. If you are interested or need further information, please contact us via or visit us in our Chaos Lab (S2|14 / 032).

List of completed theses

Effect of isospin-symmetry breaking on spectral properties

The isospin symmetry and its breaking play an important role in nuclear physics. We model the mixing of two states with different isospin quantum number by two microwave billiards, which are coupled with variable strength. One central aim is the investigation of the effect of the isospin mixing / symmetry breaking on the spectral statistics. This project is the continuation of earlier work and aims at a better understanding of the effect of symmetry breaking on certain properties of compound nucleus reactions.
This project comprises the construction of the system of two coupled microwave billiards with a variable coupling mechanism, the measurement of the spectrum under superconducting conditions and the analysis of the spectral data.

Directional emission from open dielectric resonators

Dielectric resonators with asymmetric shape are used for the construction of microlasers with directional emission. Here, the main problem is to find a tradeoff between directionality and the lifetimes of the resonances, which depend on the resonator shape. For this, circular and elliptic resonators perturbed by scatterers have been proposed.
This project involves the investigation of a circular resonator with a large scatterer or an elliptic resonator perturbed by a pointlike scatterer. Frequency spectra as well as the near- and far-field distributions are measured. Preliminary results for the circular resonator with a large scatterer already exist.

Temporal decay of regular and chaotic quantum systems

The decay of quantum systems like compound nuclei is of general interest and can be modeled by open microwave billiards with a hole in the wall. The use of superconducting resonators minimizes absorptive losses and thus the temporal decay of microwave power via the holes can be studied. Of special interest is the influence of regular or chaotic classical dynamics on the decay of the corresponding quantum system.
The project consists of the measurement of the frequency spectra of several open microwave billiards with different shapes and opening sizes under superconducting conditions and the analysis of their time spectra. It is the continuation of an earlier project, and the microwave billiards and preliminary results already exist.

Three-dimensional tube resonator

For the chaotic 3d tube resonator shown here, deviations of the spectral statistics from those of other chaotic resonators are expected. Since a large number of eigenstates for such a resonator cannot be computed reliably, it is planned to measure it experimentally, also providing a test of numerical methods.
The project consists of the construction of the tube resonator, the measurement of its spectrum under superconducting conditions and the analysis of the spectrum.

Bachelor, Diploma and Doctoral Theses

H. Alt: Untersuchung des chaotischen Verhaltens supraleitender Kavitäten (Billards) am Darmstädter Elektronenbeschleuniger S-DALINAC (1993), (Diploma Thesis).

R. Hofferbert: Untersuchung von wellendynamischen Chaos in supraleitenden Mikrowellen-Billards (1994), (Diploma Thesis).

P. Schardt: Mikrowellenexperimente zum chaotischen Verhalten eines supraleitenden Stadion-Billards und Entwicklung einer Einfangsektion am S-DALINAC (1995), (Doctoral Thesis).

H. Rehfeld: Mikrowellenexperimente zum chaotischen Verhalten von Billards aus der Familie der Pascalschen Schnecken und das Zerfallsverhalten eines Bunimovich Stadion Billards (1996), (Diploma Thesis).

C. Dembowski: Aufbau eines modularen supraleitenden Hohlraumresonators auf der Basis von verbleitem Kupfer und Anderson-Lokalisierung in Mikrowellenbillards (1997), (Diploma Thesis).

H. Alt: Gekoppelte supraleitende Mikrowellenbillards als Modellsystem für Symmetriebrechung (1998), (Doctoral Thesis).

R. Hofferbert: Wellendynamisches Chaos in einem supraleitenden 3D-Sinai-Billard und Chaos-induziertes Tunneln in einem 2D-Ring-Billard (1999), (Doctoral Thesis).

A. Heine: Untersuchung quantenchaotischer Phänomene in supraleitenden Mikrowellenbillards: Experimente mit Dreiecksbillards zum GUE-Verhalten bei zeitumkehrinvarianten Systemen (1999), (Diploma Thesis).

H. Rehfeld: Statistische Analyse und semiklassische Beschreibung von supraleitenden Limaçon-Billards und Raysplitting in supraleitenden Mikrowellenbillards (2000), (Doctoral Thesis).

C. Richter: Wellendynamisches Chaos in supraleitenden, dreidimensionalen Mikrowellenbillards (2001), (Diploma Thesis).

M. Miski-Oglu: Spatial Autocorrelation Function of Wave Functions in a Chaotic Microwave Billiard (2002), (Diploma Thesis).

C. Reese: Untersuchung von quantenchaotischen Phänomenen in regulären Billards mit kleinen Streukörpern (2002), (Diploma Thesis).

C. Dembowski: Dissipation in Mikrowellenbillards: “Exceptional Points” und Symmetriebrechung (2003), (Doctoral Thesis).

T. Friedrich: Nachweis wellenmechanischer Streuechos in offenen Mikrowellenbillards (2003), (Diploma Thesis).

A. Heine: Spektrale Untersuchungen an Mikrowellenbillards und Atomkernen (2004), (Doctoral Thesis).

F. Schäfer: Untersuchung der Zeitumkehrinvarianz in Quantenbillards (2005), (Diploma Thesis).

J. Metz: Untersuchung von Echos an “Exceptional Points” in Mikrowellenbillards (2006), (Diploma Thesis).

M. Taheri: Gekoppelte Mikrowellenbillards unterschiedlicher Größen (2006), (Diploma Thesis).

S. Bittner: Mikrowellenexperimente an dielektrischen Kreisbillards (2007), (Diploma Thesis).

T. Friedrich: Eigenschaften von Pilzbillards und Korrelationsfunktionen von Streumatrixelementen in Mikrowellenresonatoren (2007), (Doctoral Thesis).

M. Miski-Oglu: Superscars und Statistik der Knotengebiete in einem symmetrischen Barrierenbillard (2007), (Doctoral Thesis).

F. Schäfer: Time-Reversal Symmetry Breaking in Quantum Billiards (2009), (Doctoral Thesis).

P. Oria Iriarte: Double-slit experiments and decay probability in microwave billiards (2010), (Doctoral Thesis).

B. Quast: Spektrale Statistiken und dynamisches Tunneln in Billards mit konstantem Durchmesser (2010), (Diploma Thesis).

S. Bittner: Wave-dynamical properties of dielectric resonators investigated with microwaves (2010), (Doctoral Thesis).

T. Klaus: Aufbau und Messung eines supraleitenden Mikrowellen-Diracbillards (2011), (Bachelor Thesis).

C. Ripp: Untersuchung von gebundenen Zuständen in geknickten Hohlleitern (2011), (Bachelor Thesis).

J. Isensee: Experimenteller Test einer Spurformel für chaotische dielektrische Resonatoren (2011), (Bachelor Thesis).

C. Cuno Randzustände in einem supraleitenden Mikrowellen-Diracbillard (2012), (Bachelor Thesis).

Research Reports

S. Bittner: Untersuchung von Mikrowellen-Echos an zwei gekoppelten Resonatoren (2004).

P. Oria Iriarte: Vorbereitende Experimente zum Test der Riemannschen Hypothese in offenen Kreisbillards (2006).

B. Camargo: Experiments Concerning Directional Emission in Circular Dielectric Systems (2010).