Biomedical subjects

N R Cerruti

Publications and source records attributed to N R Cerruti.

3 recordsLinked to original sources

PubMed2000

Exploring phase space localization of chaotic eigenstates via parametric variation.

In a previous paper [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external parameter. The measure correlates level velocities with overlap intensities between the eigenstates and some localized state of interest. Random matrix theory predicts the absence of such correlations in chaotic systems whereas in the stadium billiard, a paradigm of chaos, strong correlations were observed. Here, we develop further the theoretical basis of that work, extend the stadium results to the full phase space, study the Planck's over 2pi dependence, and demonstrate the agreement between this measure and a semiclassical theory based on homoclinic orbits.

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PubMed2000

Phase space localization of chaotic eigenstates: violating ergodicity.

The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized nonintegrable systems. It can also serve as a measure of deviations from ergodicity due to quantum effects for typical observables. This paper relies on two well known paradigms of quantum chaos, the bakers map and the standard map, to study correlations in simple, yet chaotic, dynamical systems. The behaviors are dominated by the presence of several classical structures. These primarily include short periodic orbits and their homoclinic excursions. The dependences of the correlations deriving from perturbations allow for eigenfunction features violating ergodicity to be selectively highlighted. A semiclassical theory based on periodic orbit sums leads to certain classical correlations that are superexponentially cut off beyond a logarithmic time scale. The theory is seen to be quite successful in reproducing many of the quantum localization features.

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PubMed1999

Classical diffusion and quantum level velocities: systematic deviations from random matrix theory.

We study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic deviations from random matrix theory, assuming independence of eigenvectors from eigenvalues, are shown to be connected to classical higher-order time correlations of the chaotic system. We study the standard map as a specific example, and thus the well-known oscillatory behavior of the diffusion coefficient with respect to the parameter is reflected exactly in the oscillations of the variance of the level velocities. We study the case of mixed phase-space dynamics as well and note a transition in the scaling properties of the variance that occurs along with the classical transition to chaos.

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