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

Essays in Taxation.

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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