18 research outputs found
Chaotic dynamics and fractal structures in experiments with cold atoms
We use tools from nonlinear dynamics to the detailed analysis of cold atom
experiments. A powerful example is provided by the recent concept of basin
entropy which allows to quantify the final state unpredictability that results
from the complexity of the phase space geometry. We show here that this enables
one to reliably infer the presence of fractal structures in phase space from
direct measurements. We illustrate the method with numerical simulations in an
experimental configuration made of two crossing laser guides that can be used
as a matter wave splitter
Using the basin entropy to explore bifurcations
Bifurcation theory is the usual analytic approach to study the parameter
space of a dynamical system. Despite the great power of prediction of these
techniques, fundamental limitations appear during the study of a given problem.
Nonlinear dynamical systems often hide their secrets and the ultimate resource
is the numerical simulations of the equations. This paper presents a method to
explore bifurcations by using the basin entropy. This measure of the
unpredictability can detect transformations of phase space structures as a
parameter evolves. We present several examples where the bifurcations in the
parameter space have a quantitative effect on the basin entropy. Moreover, some
transformations, such as the basin boundary metamorphoses, can be identified
with the basin entropy but are not reflected in the bifurcation diagram. The
correct interpretation of the basin entropy plotted as a parameter extends the
numerical exploration of dynamical systems
Propagation of waves in high Brillouin zones : Chaotic branched flow and stable superwires
We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.acceptedVersionPeer reviewe
Unpredictability and basin entropy
The basin entropy is a simple idea that aims to measure the the final state unpredictability of multistable systems. Since 2016, the basin entropy has been widely used in different contexts of physics, from cold atoms to galactic dynamics. Furthermore, it has provided a natural framework to study basins of attraction in nonlinear dynamics and new criteria for the detection of fractal boundaries. In this article, we describe the concept as well as fundamental applications. In addition, we provide our perspective on the future challenges of applying the basin entropy idea to understanding complex systems
Contribution a l'identification structurale : adequation d'un modele mathematique a des resultats d'essais
SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc