4 research outputs found
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
Engineering fidelity echoes in Bose-Hubbard Hamiltonians
We analyze the fidelity decay for a system of interacting bosons described by
a Bose-Hubbard Hamiltonian. We find echoes associated with "non-universal"
structures that dominate the energy landscape of the perturbation operator.
Despite their classical origin, these echoes persist deep into the quantum
(perturbative) regime and can be described by an improved random matrix
modeling. In the opposite limit of strong perturbations (and high enough
energies), classical considerations reveal the importance of self-trapping
phenomena in the echo efficiency.Comment: 6 pages, use epl2.cls class, 5 figures Cross reference with nlin,
quant-phy
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