Algebraic fidelity decay for local perturbations

From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as {\em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.Comment: 4 pages, 5 figure

Nodal domains in open microwave systems

Nodal domains are studied both for real $\psi_R$ and imaginary part $\psi_I$ of the wavefunctions of an open microwave cavity and found to show the same behavior as wavefunctions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase $\phi_g$ according to $\psi_R+i\psi_I=e^{i\phi_g}(\psi_R'+i\psi_I')$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.Comment: 7 pages, 10 figures, submitted to PR

Dynamical tunneling in mushroom billiards

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.Comment: 4 pages, 4 figure

Resonance widths in open microwave cavities studied by harmonic inversion

From the measurement of a reflection spectrum of an open microwave cavity the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this it became possible to resolve the resonances in a regime where the line widths exceed the mean level spacing up to a factor of 10, a value inaccessible in experiments up to now. The obtained experimental distributions of line widths were found to be in perfect agreement with predictions from random matrix theory when wall absorption and fluctuations caused by couplings to additional channels are considered.Comment: 4 pages, 6 figure

On the theory of cavities with point-like perturbations. Part I: General theory

The theoretical interpretation of measurements of "wavefunctions" and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as "point-like perturbations". This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of "wavefunction measurements". This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized'' Green function, which contains the information on boundary reflections and has no singularity inside the cavity.Comment: 23 pages, 6 figure

Density and Correlation functions of vortex and saddle points in open billiard systems

We present microwave measurements for the density and spatial correlation of current critical points in an open billiard system, and compare them with the predictions of the Random Wave Model (RWM). In particular, due to a novel improvement of the experimental set-up, we determine experimentally the spatial correlation of saddle points of the current field. An asymptotic expression for the vortex-saddle and saddle-saddle correlation functions based on the RWM is derived, with experiment and theory agreeing well. We also derive an expression for the density of saddle points in the presence of a straight boundary with general mixed boundary conditions in the RWM, and compare with experimental measurements of the vortex and saddle density in the vicinity of a straight wall satisfying Dirichlet conditions.Comment: submitted to Physical Review

Classical wave experiments on chaotic scattering

We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems, scattering theory has to be applied for a quantitative interpretation of the measurements. Most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation. In all studied examples a quantitative agreement between experiment and theory is achieved. To this end it is necessary, however, to take absorption and imperfect coupling into account, concepts that were ignored in most previous theoretical investigations. Classical phase space signatures of scattering are being examined in a small number of experiments.Comment: 33 pages, 13 figures; invited review for the Special Issue of J. Phys. A: Math. Gen. on "Trends in Quantum Chaotic Scattering

Besonderheiten, Bedingungsfaktoren und Barrieren multiprofessionellen Lehrens und Lernens von Gesundheits- und Nicht-Gesundheitsberufen: Eine explorative Befragung aus Sicht der Lehrenden

Objective: Care for people with dementia is considered a multi-professional challenge that requires a collaborative approach between health professionals and non-health professionals. Didactic strategies to ensure the same qualifications across these occupational groups are lacking. This article presents the joint learning of selected properties and promotive and obstructive conditions, using the example of a multi-professional Master's programme. It subsequently draws conclusions for didactic concepts.Methodology: The perceptions of 12 teachers on this Master's programme, all representing different professions, were determined by using a qualitative exploratory survey on the three stated dimensions. With the aid of a summarising content analysis, their statements were condensed and abstracted so as to deduce appropriate requirements for methodical and didactic learning scenarios.Results: In view of the fact that the students have very varied previous knowledge, the main challenge is finding a balance between expertise and tediousness. Establishing essential and common expertise, as well as sensitivity for different perspectives, is made particularly difficult by the fact that health and non-health professions differ greatly in terms of methods and approaches. For a successful outcome, the content focal points and didactic and methodical concepts for a learning group need to take into account the composition of that specific group. Recourse to didactic standard concepts is only possible to a limited extent. Conclusions: The aim of joint teaching and learning of health and non-health professionals is to enhance the understanding of a profession: This is done by making individuals aware of their role in the chain of care, so they can recognise and organise the mutual conditionality of their own and external professional contributions.Zielsetzung: Die Versorgung von Menschen mit Demenz gilt als multiprofessionelle Herausforderung, die eine kollaborative Gestaltung der Gesundheits- und Nicht-Gesundheitsberufe erfordert. Didaktische Konzepte zur gemeinsamen Qualifizierung dieser Berufsgruppen fehlen. Der Beitrag zeigt ausgewählte Besonderheiten, Barrieren und Bedingungsfaktoren deren gemeinsamen Lernens am Beispiel eines multiprofessionellen Masterstudiengangs auf und zieht Konsequenzen für didaktische Konzepte.Methodik: Die Einschätzungen von 12 Lehrenden dieses Masterstudiengangs, die unterschiedliche Professionen repräsentieren, wurden mit einer qualitativ-explorativen Befragung zu den genannten drei Dimensionen ermittelt. Mit Hilfe einer zusammenfassenden Inhaltsanalyse wurden deren Aussagen kondensiert und abstrahiert, um Anforderungen an geeignete methodisch-didaktische Lernszenarien abzuleiten.Ergebnisse: Vor dem Hintergrund sehr divergierenden Vorwissens der Studierenden besteht die zentrale Herausforderung darin, eine Balance zwischen Expertise und Langeweile zu finden. Das Herstellen notwendiger gemeinsamer Gegenstandsverständnisse und Sensibilität für unterschiedliche Perspektiven ist besonders dadurch erschwert, dass Gesundheits- und Nicht-Gesundheitsberufe sich in ihren Arbeits- und Herangehensweisen stark unterscheiden. Zur Zielerreichung sind je nach Zusammensetzung der Lerngruppe unterschiedlich konturierte inhaltliche Schwerpunkte und didaktisch-methodische Konzepte notwendig. Ein Rückgriff auf didaktische Regelkonzepte ist nur begrenzt möglich. Schlussfolgerungen: Das gemeinsame Lehren und Lernen von Gesundheits- und Nicht-Gesundheitsberufen zielt auf ein erweitertes Berufsverständnis ab: Durch die Wahrnehmung als Teil der Versorgungskette, die wechselseitige Bedingtheit der eigenen und fremden Professionsbeiträge zu erkennen und zu gestalten