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.Comment: Submitted to Phys. Rev. E without the appendi

Parabolic manifolds in the scattering map and direct quantum processes

International audienceWe analyse the quantum effects of parabolic manifolds in Jung's iterated scattering map. For this purpose we consider the classical map proposed previously to be the exact classical analogue of Rydberg molecules calculated with the approximations relevant to the multichannel quantum defect theory for energies above the ionization threshold. The part corresponding to positive electron energies can be viewed as a Jung scattering map without the trivial direct processes. This map contains a parabolic manifold of fixed points which gives rise to a regular series of quantum states which behave very much like eigenchannels that miss the target

Compatibility of Kura Clover and Cool Season Grass Mixtures in Michigan

Kura clover (Trifolium ambiguum Bieb.) is an alternative forage legume for rotational grazing in cool-season grass mixtures. However, compatibility with cool-season grasses is unknown. Seven cool-season perennial grasses were seeded into Kura clover in a rotational grazing experiment. The objectives of this study were to evaluate botanical composition, forage yield and quality of binary mixtures of cool-season grass with Kura clover. Field studies were conducted on a Nester (fine sandy loam) soil at Lake City Experiment Station, Lake City, MI. Botanical compositions in the first year of the study heavily favored grasses (avg. 74%) and Kura clover accounted for less than 20%. Crude protein (CP) concentration was negatively related with grass composition (r = -0.69**), however, positively related with Kura clover composition (r = 0.60**). Perennial ryegrass (Lolium perenne L.) was superior in total forage yield and good forage quality, while reed canarygrass (Phalaris arundinacea L.) was the least desirable species

Cool-Season Grass Response to Increasing Nitrogen Fertiliser Rates in Michigan

Nitrogen (N) fertility recommendations for cool-season grasses in the north central region of the USA have not been species specific. This broad recommendation assumes that all grasses have similar N demands, while seasonal growth patterns and dry matter yield of cool-season grass species vary. Nitrogen fertiliser costs have steadily increased, but recommendations are to be below optimal levels for economic return (Klausner et al., 1998). A more specific N fertiliser recommendation may increase the producers’ net income

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.Comment: 4 pages, 5 .eps figure

Chaotic Scattering in the Regime of Weakly Overlapping Resonances

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz

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.Comment: 4 pages, 4 figure

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.Comment: RevTex 4.0, 5 eps-figure