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Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic…
Basin entropy: a new tool to analyze uncertainty in dynamical systems
- Alvar Daza, A. Wagemakers, B. Georgeot, D. Guéry-Odelin, M. Sanjuán
- Computer ScienceScientific reports
- 8 May 2016
The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied and provides a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.
Asymptotic analysis of high-frequency acoustic modes in rapidly rotating stars
The asteroseismology of rapidly rotating pulsating stars is hindered by our poor knowledge of the effect of the rotation on the oscillation properties. Here we present an asymptotic analysis of…
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality.
- I. García-Mata, O. Giraud, B. Georgeot, J. Martín, R. Dubertrand, G. Lemarié
- Physics, MathematicsPhysical review letters
- 9 September 2016
The Anderson transition is studied on a generic model of random graphs with a tunable branching parameter 1<K<2, and a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales.
Spectral properties of the Google matrix of the World Wide Web and other directed networks
- B. Georgeot, O. Giraud, D. Shepelyansky
- Computer SciencePhysical review. E, Statistical, nonlinear, and…
- 17 February 2010
Numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks are studied, including the PageRank.
Integrability and Quantum Chaos in Spin Glass Shards
We study spin glass clusters ("shards") in a random transverse magnetic field, and determine the regime where quantum chaos and random matrix level statistics emerge from the integrable limits of…
Analysis of singular inertial modes in a spherical shell: the slender toroidal shell model
We derive the asymptotic spectrum (as the Ekman number E → 0) of axisymmetric inertial modes when the problem is restricted to two dimensions. We show that the damping rate of such modes scales with…
Breit-Wigner Width and Inverse Participation Ratio in Finite Interacting Fermi Systems
For many-body Fermi systems we determine the dependence of the Breit-Wigner width and inverse participation ratio (IPR) on interaction strength U > Uc and energy excitation dE > dE_ch when a…
Wave chaos in rapidly rotating stars.
The dynamics of acoustic rays in rotating polytropic stars are studied and it is shown using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions.
Exponential gain in quantum computing of quantum chaos and localization.
We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos,…