arXiv subjects

B. Dietz

Publications and source records attributed to B. Dietz.

48 records · Page 3Linked to original sources

arXiv2007

Spectral properties of Bunimovich mushroom billiards

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the nearest-neighbor spacing distribution. Theoretical predictions for the quantum properties of mixed systems rely on the sharp separability of phase space - an unusual property met by mushroom billiards. We however find deviations which are ascribed to the presence of dynamic tunneling.

nlin.CD↗

arXiv2007

Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards

Using reciprocity, we investigate the breaking of time-reversal (T) symmetry due to a ferrite embedded in a flat microwave billiard. Transmission spectra of isolated single resonances are not sensitive to T-violation whereas those of pairs of nearly degenerate resonances do depend on the direction of time. For their theoretical description a scattering matrix model from nuclear physics is used. The T-violating matrix elements of the effective Hamiltonian for the microwave billiard with the embedded ferrite are determined experimentally as functions of the magnetization of the ferrite.

cond-mat.other↗

arXiv2006

Rabi Oscillations at Exceptional Points in Microwave Billiards

We experimentally investigated the decay behavior with time t of resonances near and at exceptional points, where two complex eigenvalues and also the associated eigenfunctions coalesce. The measurements were performed with a dissipative microwave billiard, whose shape depends on two parameters. The t^2-dependence predicted at the exceptional point on the basis of a two-state matrix model could be verified. Outside the exceptional point the predicted Rabi oscillations, also called quantum echoes in this context, were detected. To our knowledge this is the first time that quantum echoes related to exceptional points were observed experimentally.

cond-mat.other↗

arXiv2006

First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard

With a perturbation body technique intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside up to mode numbers as large as about 700 were measured. A method for the reconstruction of the amplitudes and phases of the electric field strength from those intensity distributions has been developed. Recently predicted superscars have been identified experimentally and - using the well known analogy between the electric field strength and the quantum mechanical wave function in a two-dimensional microwave billiard - their properties determined.

nlin.CD↗

arXiv2006

Nonperiodic echoes from mushroom billiard hats

Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.

nlin.CD↗

arXiv2006

Spectral statistics in an open parametric billiard system

We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal ensembles of random matrices are found. They are explained by treating the billiard as an open scattering system in which microwave power is coupled in and out via antennas. To study the interaction of the quantum (or wave) system with its environment a highly sensitive parametric correlator is used.

cond-mat.mes-hall↗

arXiv2004

First experimental evidence for quantum echoes in scattering systems

A self-pulsing effect termed quantum echoes has been observed in experiments with an open superconducting and a normal conducting microwave billiard whose geometry provides soft chaos, i.e. a mixed phase space portrait with a large stable island. For such systems a periodic response to an incoming pulse has been predicted. Its period has been associated to the degree of development of a horseshoe describing the topology of the classical dynamics. The experiments confirm this picture and reveal the topological information.

nlin.CD↗

arXiv2004

Encircling an Exceptional Point

We calculate analytically the geometric phases that the eigenvectors of a parametric dissipative two-state system described by a complex symmetric Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a parameter setting where the two eigenvalues and the corresponding eigenvectors of the Hamiltonian coalesce. We show that it can be encircled on a path along which the eigenvectors remain approximately real and discuss a microwave cavity experiment, where such an encircling of an EP was realized. Since the wavefunctions remain approximately real, they could be reconstructed from the nodal lines of the recorded spatial intensity distributions of the electric fields inside the resonator. We measured the geometric phases that occur when an EP is encircled four times and thus confirmed that for our system an EP is a branch point of fourth order.

nlin.CD↗

arXiv2003

Comment on ''Exceptional points and double poles of the S matrix''

In a recent paper [Phys. Rev. E 67, 026204 (2003)], Rotter calculates the geometric phases that are picked up by the eigenvectors of a two-state quantum system when an exceptional point is encircled. In addition to the geometric phases observed by Dembowski et al. in a microwave cavity experiment [Phys. Rev. Lett. 86, 787 (2001)], she finds a phase factor of i. We show that Rotters results are inconsistent.

nlin.CD↗

arXiv2003

Observation of a Chiral State in a Microwave Cavity

A microwave experiment has been realized to measure the phase difference of the oscillating electric field at two points inside the cavity. The technique has been applied to a dissipative resonator which exhibits a singularity -- called exceptional point -- in its eigenvalue and eigenvector spectrum. At the singularity, two modes coalesce with a phase difference of $π/2 .$ We conclude that the state excited at the singularity has a definitiv chirality.

nlin.CD↗

arXiv2003

Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry

The spectral properties of a two-dimensional microwave billiard showing threefold symmetry have been studied with a new experimental technique. This method is based on the behavior of the eigenmodes under variation of a phase shift between two input channels, which strongly depends on the symmetries of the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been identified by a simple and purely experimental method. This set clearly shows Gaussian unitary ensemble statistics, although the system is time-reversal invariant.

nlin.CD↗

arXiv2002

Experimental Test of a Trace Formula for a Chaotic Three Dimensional Microwave Cavity

We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuation properties. The experimental length spectrum exhibits contributions from periodic orbits of non-generic modes and from unstable periodic orbit of the underlying classical system. It is well reproduced by our theoretical calculations based on the trace formula derived by Balian and Duplantier for chaotic electromagnetic cavities.

nlin.CD↗