4 research outputs found
Scattering fidelity in elastodynamics
The recent introduction of the concept of scattering fidelity, causes us to
revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302
(2003)]. There, the ``distortion'' of the coda of an acoustic signal is
measured under temperature changes. This quantity is in fact the negative
logarithm of scattering fidelity. We re-analyse their experimental data for two
samples, and we find good agreement with random matrix predictions for the
standard fidelity. Usually, one may expect such an agreement for chaotic
systems only. While the first sample, may indeed be assumed chaotic, for the
second sample, a perfect cuboid, such an agreement is more surprising. For the
first sample, the random matrix analysis yields a perturbation strength
compatible with semiclassical predictions. For the cuboid the measured
perturbation strength is much larger than expected, but with the fitted values
for this strength, the experimental data are well reproduced.Comment: 4 page
Fidelity amplitude of the scattering matrix in microwave cavities
The concept of fidelity decay is discussed from the point of view of the
scattering matrix, and the scattering fidelity is introduced as the parametric
cross-correlation of a given S-matrix element, taken in the time domain,
normalized by the corresponding autocorrelation function. We show that for
chaotic systems, this quantity represents the usual fidelity amplitude, if
appropriate ensemble and/or energy averages are taken. We present a microwave
experiment where the scattering fidelity is measured for an ensemble of chaotic
systems. The results are in excellent agreement with random matrix theory for
the standard fidelity amplitude. The only parameter, namely the perturbation
strength could be determined independently from level dynamics of the system,
thus providing a parameter free agreement between theory and experiment
A trivial observation on time reversal in random matrix theory
It is commonly thought that a state-dependent quantity, after being averaged
over a classical ensemble of random Hamiltonians, will always become
independent of the state. We point out that this is in general incorrect: if
the ensemble of Hamiltonians is time reversal invariant, and the quantity
involves the state in higher than bilinear order, then we show that the
quantity is only a constant over the orbits of the invariance group on the
Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure
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