5,209 research outputs found
Structural Invariance and the Energy Spectrum
We extend the application of the concept of structural invariance to bounded
time independent systems. This concept, previously introduced by two of us to
argue that the connection between random matrix theory and quantum systems with
a chaotic classical counterpart is in fact largely exact in the semiclassical
limit, is extended to the energy spectra of bounded time independent systems.
We proceed by showing that the results obtained previously for the
quasi-energies and eigenphases of the S-matrix can be extended to the
eigenphases of the quantum Poincare map which is unitary in the semiclassical
limit. We then show that its eigenphases in the chaotic case move rather
stiffly around the unit circle and thus their local statistical fluctuations
transfer to the energy spectrum via Bogomolny's prescription. We verify our
results by studying numerically the properties of the eigenphases of the
quantum Poincare map for billiards by using the boundary integral method.Comment: 10 pages, 5 figure
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
Doorway States and Billiards
Whenever a distinct state is immersed in a sea of complicated and dense
states, the strength of the distinct state, which we refer to as a doorway, is
distributed in their neighboring states. We analyze this mechanism for 2-D
billiards with different geometries. One of them is symmetric and integrable,
another is symmetric but chaotic, and the third has a capricious form. The fact
that the doorway-state mechanism is valid for such highly diverse cases, proves
that it is robust.Comment: 7 pages, 6 figures, Accepted in Proceedings of "Symmetries in
Nature", Symposium in Memoriam Marcos Moshinsk
Invariant Manifolds and Collective Coordinates
We introduce suitable coordinate systems for interacting many-body systems
with invariant manifolds. These are Cartesian in coordinate and momentum space
and chosen such that several components are identically zero for motion on the
invariant manifold. In this sense these coordinates are collective. We make a
connection to Zickendraht's collective coordinates and present certain
configurations of few-body systems where rotations and vibrations decouple from
single-particle motion. These configurations do not depend on details of the
interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st
Preventing adolescents’ externalizing and internalizing symptoms : effects of the Penn Resiliency Program
This study reports secondary outcome analyses from a past study of the Penn Resiliency
Program (PRP), a cognitive-behavioral depression prevention program for middle-school
aged children. Middle school students (N = 697) were randomly assigned to PRP, PEP
(an alternate intervention), or control conditions. Gillham et al., (2007) reported analyses
examining PRP’s effects on average and clinical levels of depression symptoms. We
examine PRP’s effects on parent-, teacher-, and self-reports of adolescents’ externalizing
and broader internalizing (depression/anxiety, somatic complaints, and social
withdrawal) symptoms over three years of follow-up. Relative to no intervention control,
PRP reduced parent-reports of adolescents’ internalizing symptoms beginning at the first
assessment after the intervention and persisting for most of the follow-up assessments.
PRP also reduced parent-reported conduct problems relative to no-intervention. There
was no evidence that the PRP program produced an effect on teacher- or self-report of
adolescents’ symptoms. Overall, PRP did not reduce symptoms relative to the alternate
intervention, although there is a suggestion of a delayed effect for conduct problems.
These findings are discussed with attention to developmental trajectories and the
importance of interventions that address common risk factors for diverse forms of
negative outcomes.peer-reviewe
- …