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International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves

Superscars in Barrier Billiard - Phenomenon Induced by Diffraction

M. Miski-Oglu

Published Jun 1, 2007• 0 citations
Publisher

Abstract

Here is presented an experimental investigation of superscars in a quantum barrier billiard.The experimental observation of the superscars requires (i) the detection of eigenmodes at sufficiently high quantum numbers N and (ii) the resolution of all modes up to these quantum numbers.
DOI
10.1109/msmw.2007.4294750

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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.
In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which sensitively affects the strength function. The recently measured superscars in the barrier billiard provide an ideal model for an in-depth investigation of this mechanism. We introduce two new statistical observables: the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using random matrix theory and random plane waves, we obtain a consistent understanding of the experimental data.
The recently measured superscars in a pseudointegrable barrier billiard [Phys. Rev. Lett. 97, 254102 (2006)] serve as a paradigm for strength function phenomena known in a variety of open mesoscopic quantum systems ranging from atoms to nuclei. The superscarring state is thereby of a simple structure whose strength is spread over the many other nonscarring chaotic states in the billiard, i.e. it acts as a so called doorway state. In this talk the observed spreading of four different superscars is briefly discussed in terms of a model based on Random Matrix Theory and also by investigating the spatial correlations of the measured wave functions. It is shown that the results derived are fully consistent with each other. Furthermore, some properties of the nodal domains of the experimental wave functions are analyzed. It is found that the mean value of the rescaled nodal domains shows a deviation from what is expected from a percolation model. This deviation can, however, be qualitatively understood in terms of the doorway state picture.
We demonstrate experimentally the existence and significance of diffractive orbits in an open microwave billiard. Orbits that diffract off a sharp edge strongly influence the conduction spectrum, especially in the regime where there are no stable classical orbits. On resonance, the wave functions are influenced by both classical and diffractive orbits. Off resonance, the wave functions are determined by the constructive interference of multiple transient orbits. The experimental results agree well with quantum computations and with a semiclassical theory that incorporates diffraction.
In this work we study the eigenstates and the energy spectra of a generic billiard system with the use of microwave resonators.This is possible due to the exact correspondence between the Schrödinger equation and the electric field equations of the lowest modes in thin microwave resonators.We obtain a good agreement between the numerical (exact) and experimental eigenstates, while the short range experimental spectral statistics show the expected Brody-like behaviour in this energy range, as opposed to the Berry-Robnik picture which is valid only in the semiclassical region of sufficiently small effective Planck's constant.