94 research outputs found
Web-assisted tunneling in the kicked harmonic oscillator
We show that heating of harmonically trapped ions by periodic delta kicks is
dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these
values, quasienergy eigenstates localized on island structures undergo avoided
crossings with extended web-states.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. Let
Dynamical Stability and Quantum Chaos of Ions in a Linear Trap
The realization of a paradigm chaotic system, namely the harmonically driven
oscillator, in the quantum domain using cold trapped ions driven by lasers is
theoretically investigated. The simplest characteristics of regular and chaotic
dynamics are calculated. The possibilities of experimental realization are
discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev
Fractional Fourier detection of L\'evy Flights: application to Hamiltonian chaotic trajectories
A signal processing method designed for the detection of linear (coherent)
behaviors among random fluctuations is presented. It is dedicated to the study
of data recorded from nonlinear physical systems. More precisely the method is
suited for signals having chaotic variations and sporadically appearing regular
linear patterns, possibly impaired by noise. We use time-frequency techniques
and the Fractional Fourier transform in order to make it robust and easily
implementable. The method is illustrated with an example of application: the
analysis of chaotic trajectories of advected passive particles. The signal has
a chaotic behavior and encounter L\'evy flights (straight lines). The method is
able to detect and quantify these ballistic transport regions, even in noisy
situations
Global Superdiffusion of Weak Chaos
A class of kicked rotors is introduced, exhibiting accelerator-mode islands
(AIs) and {\em global} superdiffusion for {\em arbitrarily weak} chaos. The
corresponding standard maps are shown to be exactly related to generalized web
maps taken modulo an ``oblique cylinder''. Then, in a case that the web-map
orbit structure is periodic in the phase plane, the AIs are essentially {\em
normal} web islands folded back into the cylinder. As a consequence, chaotic
orbits sticking around the AI boundary are accelerated {\em only} when they
traverse tiny {\em ``acceleration spots''}. This leads to chaotic flights
having a quasiregular {\em steplike} structure. The global weak-chaos
superdiffusion is thus basically different in nature from the strong-chaos one
in the usual standard and web maps.Comment: REVTEX, 4 Figures: fig1.jpg, fig2.ps, fig3.ps, fig4.p
Edge of chaos of the classical kicked top map: Sensitivity to initial conditions
We focus on the frontier between the chaotic and regular regions for the
classical version of the quantum kicked top. We show that the sensitivity to
the initial conditions is numerically well characterised by , where , and
is the -generalization of the Lyapunov coefficient, a result
that is consistent with nonextensive statistical mechanics, based on the
entropy ). Our analysis
shows that monotonically increases from zero to unity when the kicked-top
perturbation parameter increases from zero (unperturbed top) to
, where . The entropic index remains equal
to unity for , parameter values for which the phase space
is fully chaotic.Comment: To appear in "Complexity, Metastability and Nonextensivity" (World
Scientific, Singapore, 2005), Eds. C. Beck, A. Rapisarda and C. Tsalli
- âŠ