5 research outputs found
Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices
The problem of chaotic scattering in presence of direct processes or prompt
responses is mapped via a transformation to the case of scattering in absence
of such processes for non-unitary scattering matrices, \tilde S. In the absence
of prompt responses, \tilde S is uniformly distributed according to its
invariant measure in the space of \tilde S matrices with zero average, < \tilde
S > =0. In the presence of direct processes, the distribution of \tilde S is
non-uniform and it is characterized by the average (\neq 0). In
contrast to the case of unitary matrices S, where the invariant measures of S
for chaotic scattering with and without direct processes are related through
the well known Poisson kernel, here we show that for non-unitary scattering
matrices the invariant measures are related by the Poisson kernel squared. Our
results are relevant to situations where flux conservation is not satisfied.
For example, transport experiments in chaotic systems, where gains or losses
are present, like microwave chaotic cavities or graphs, and acoustic or elastic
resonators.Comment: Added two appendices and references. Corrected typo
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
Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities
We consider the statistics of the impedance Z of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental Z data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized impedance whose probability density function is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We find that impedance fluctuations decrease with increasing loss. The results apply to scattering measurements on any wave chaotic system
Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities
We consider the statistics of the impedance Z of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental Z data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized impedance whose probability density function is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We find that impedance fluctuations decrease with increasing loss. The results apply to scattering measurements on any wave chaotic system
Aspects of the scattering and impedance properties of chaotic microwave cavities. Acta Physica Polonica A
We consider the statistics of the impedance Z of a chaotic microwave cavity coupled to a single port. We remove the non-universal effects of the coupling from the experimental Z data using the radiation impedance obtained directly from the experiments. We thus obtain the normalized impedance whose probability density function is predicted to be universal in that it depends only on the loss (quality factor) of the cavity. We find that impedance fluctuations decrease with increasing loss. The results apply to scattering measurements on any wave chaotic system