arXiv subjects

U. Kuhl

Publications and source records attributed to U. Kuhl.

53 records · Page 3Linked to original sources

arXiv2006

Nodal domains in open microwave systems

Nodal domains are studied both for real $ψ_R$ and imaginary part $ψ_I$ 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 $ϕ_g$ according to $ψ_R+iψ_I=e^{iϕ_g}(ψ_R'+iψ_I')$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.

cond-mat.other↗

arXiv2005

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.

cond-mat.mes-hall↗

arXiv2005

Design of beam splitters and microlasers using chaotic waveguides

We consider waveguides formed by single or multiple two-dimensional chaotic cavities connected to leads. The cavities are chaotic in the sense that the ray (or equivalently, classical particle) dynamics within them is chaotic. Geometrical parameters are chosen to produce a mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Incoming rays (or particles) cannot penetrate into these islands but incoming plane waves dynamically tunnel into them at a certain discrete set of frequencies (energies). The support of the corresponding quasi-bound states is along the trajectories of periodic orbits trapped within the cavity. We take advantage of this difference in the ray/wave behavior to demonstrate how chaotic waveguides can be used to design beam splitters and microlasers. We also present some preliminary experimental results in a microwave realization of such chaotic waveguide.

physics.optics↗

arXiv2005

1/f noise in experimental Sinai quantum billiards

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. In this Letter we show that the level fluctuations of experimental realizations of the Sinai billiard exhibit {\em 1/f} noise, corroborating the conjecture. Assuming that the statistical properties of these systems are those of the Gaussian orthogonal ensemble (GOE), we compare the experimental results with the universal behavior predicted in the random matrix framework, and find an excellent agreement. The deviations from this behavior observed at low frequencies can be easily explained with the semiclassical periodic orbit theory. In conclusion, it is shown that the main features of the conjecture are affected neither by non-universal properties due to the underlying classical dynamics nor by the uncertainties of the experimental setup.

cond-mat.mes-hall↗

arXiv2004

Fano resonances and decoherence in transport through quantum dots

A tunable microwave scattering device is presented which allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. We observe a non-monotonic evolution of resonance parameters that is explained in terms of interacting resonances. The dissipation of radiation in the cavity walls leads to decoherence and thus to a modification of the Fano profile. We show that the imaginary part of the complex Fano q-parameter allows to determine the absorption constant of the cavity. Our theoretical results demonstrate further that the two decohering mechanisms, dephasing and dissipation, are equivalent in terms of their effect on the evolution of Fano resonance lineshapes.

cond-mat.mes-hall↗

arXiv2004

Signatures of Dynamical Tunneling in the Wave function of a Soft-Walled Open Microwave Billiard

Evidence for dynamical tunneling is observed in studies of the transmission, and wave functions, of a soft-walled microwave cavity resonator. In contrast to previous work, we identify the conditions for dynamical tunneling by monitoring the evolution of the wave function phase as a function of energy, which allows us to detect the tunneling process even under conditions where its expected level splitting remains irresolvable.

cond-mat.mes-hall↗

arXiv2004

Measurement of long-range wavefunction correlations in an open microwave billiard

We investigate the statistical properties of wavefunctions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wavefunctions cross over from real to complex. The distribution of the phase rigidity, which characterizes the degree to which a wavefunction is complex, and long-range correlations of intensity and current density are studied as a function of the number of channels in the openings. All measured quantities are in perfect agreement with theoretical predictions.

cond-mat.mes-hall↗

arXiv2004

Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption

We quantify the presence of direct processes in the S-matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{iθ}, is studied in cavities with time-reversal symmetry for different antenna coupling strengths T_a or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations based on the Heidelberg approach including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with random-matrix predictions for all cases.

cond-mat.mes-hall↗

arXiv2003

Tunable Fano Resonances in Transport through Microwave Billiards

We present a tunable microwave scattering device that allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. Transport in this device is nearly fully coherent. By comparison with quantum calculations, employing the modular recursive Green's-function method, the scattering wave function and the degree of residual decoherence can be determined. The parametric variation of Fano line shapes in terms of interacting resonances is analyzed.

cond-mat.mes-hall↗

arXiv2003

Distribution of reflection coefficients in absorbing chaotic microwave cavities

The distributions of the reflection coefficients $P(R)$ for chaotic microwave cavities with time-reversal symmetry are investigated in different absorption and antenna coupling regimes. In all investigated regimes the agreement between the experimental distributions and random matrix result is very good, provided both the antenna coupling $T_a$ and wall absorption strength $T_w$ are properly accounted for. Those parameters are determined by independent experimental quantities.

cond-mat.mes-hall↗

arXiv2003

Scanning Fourier Spectroscopy: A microwave analog study to image transmission paths in quantum dots

We use a microwave cavity to investigate the influence of a movable absorbing center on the wave function of an open quantum dot. Our study shows that the absorber acts as a position-selective probe, which may be used to suppress those wave function states that exhibit an enhancement of their probability density near the region where the impurity is located. For an experimental probe of this wave function selection, we develop a technique that we refer to as scanning Fourier spectroscopy, which allows us to identify, and map out, the structure of the classical trajectories that are important for transmission through the cavity.

cond-mat.mes-hall↗

arXiv2003

Current and vorticity auto correlation functions in open microwave billiards

Using the equivalence between the quantum-mechanical probability density in a quantum billiard and the Poynting vector in the corresponding microwave system, current distributions were studied in a quantum dot like cavity, as well as in a Robnik billiard with lambda=0.4, and an introduced ferrite cylinder. Spatial auto correlation functions for currents and vorticity were studied and compared with predictions from the random-superposition-of-plane-waves hypothesis. In addition different types of vortex neighbour spacing distributions were determined and compared with theory.

cond-mat.mes-hall↗

arXiv1999

Experimental observation of the mobility edge in a waveguide with correlated disorder

The tight-binding model with correlated disorder introduced by Izrailev and Krokhin [PRL 82, 4062 (1999)] has been extended to the Kronig-Penney model. The results of the calculations have been compared with microwave transmission spectra through a single-mode waveguide with inserted correlated scatterers. All predicted bands and mobility edges have been found in the experiment, thus demonstrating that any wanted combination of transparent and non-transparent frequency intervals can be realized experimentally by introducing appropriate correlations between scatterers.

cond-mat.dis-nn↗

arXiv1999

Global and local level dynamics in chaotic microwave billiards

The spectra of Sinai microwave billiards and rectangular billiards with statistically distributed circular scatterers have been taken as a function of the position of one wall, and of one of the scatterers, respectively. Whereas in the first case the velocity distribution and correlations obey the universal behaviour predicted by Simons and Altshuler, in the second case a completely different behaviour is observed. This is due to the fact that a shift of one wall changes the wave function globally whereas the displacement of one scatterer only leads to a local perturbance.

cond-mat↗

arXiv1999

Correlations of electromagnetic fields in chaotic cavities

We consider the fluctuations of electromagnetic fields in chaotic microwave cavities. We calculate the transversal and longitudinal correlation function based on a random wave assumption and compare the predictions with measurements on two- and three-dimensional microwave cavities.

chao-dyn↗

arXiv1999

Global versus local billiard level dynamics: The limits of universality

Level dynamics measurements have been performed in a Sinai microwave billiard as a function of a single length, as well as in rectangular billiards with randomly distributed disks as a function of the position of one disk. In the first case the field distribution is changed globally, and velocity distributions and autocorrelation functions are well described by universal functions derived by Simons and Altshuler. In the second case the field distribution is changed locally. Here another type of universal correlations is observed. It can be derived under the assumption that chaotic wave functions may be described by a random superposition of plane waves.

cond-mat↗

arXiv1997

Distribution of the wave function inside chaotic partially open systems

We demonstrate both theoretically and experimentally that the distribution of the wavefunction inside a partially open chaotic timereversal symmetric system displays significant deviations from the Porter Thomas distribution. We give arguments which show that this distribution resembles the distribution which is expected to be found in closed chaotic systems with broken time reversal symmetry.

chao-dyn↗