Non-linear Dynamics in complex systems: deterministic and stochastic aspects
Organization: J.C. Garreau (PhLAM)
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Guillaume Berthet Laboratoire Charles Fabry, Institut d'Optique Palaiseau
Marcus Werner Beims Universidade Federal de Curitiba (Brazil)
In this talk I present the parameter space of a discrete ratchet model which gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures, where larger currents are usually observed inside, appear along preferred direction in the parameter space giving a guide to follow the current. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Results about the thermal and vacuum fluctuations effects on classical and quantum ratchet currents, respectively, are presented.
Rob Nyman Imperial College London
Miguel Onorato Universita di Torino
I will present some new theoretical results on the original Fermi-Pasta-Ulam (FPU) system with N=16,32 and 642 masses connected by a nonlinear quadratic spring. The approach is based on resonant wave-wave interaction theory, i.e. I assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the FPU equation of motion, I will show that the first non trivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. The time scale of such interactions is extremely large and it is of the order of $1/\epsilon^8$, where $\epsilon$ is the small parameter in the system. The results are supported by extensive numerical simulations.
Cord Müller University of Konstanz (Germany) et Nice Nonlinear Institute (France)
In this talk, I will introduce a new framework to study weak localization as well as the onset of Anderson localization in disordered systems. The idea is to expose the waves propagating in a random scattering environment to a sequence of short dephasing pulses. The system responds through coherence peaks forming at specific echo times, each echo representing a particular process of quantum interference. We have suggested a concrete realization for cold gases, where quantum interferences are observed in the momentum distribution of matter waves in a laser speckle potential. Our proposal has been recently realised at Institut d’Optique in the weak localisation regime. Eventually, we envisage the probing of higher-order processes like coherent-forward scattering, which has been established as the momentum-space signature of Anderson localisation. Reference: T. Mickliltz, C.A. Mueller, A. Altland, arXiv:1406.6915
Stefano Trillo Universita di Ferrara (Italy)
Dispersive shock waves (DSWs) entails the breaking of a wave disturbance through the spontaneous emission of fast oscillations (wavetrains) caused by a weak dispersion in response to the tendency of a nonlinear system to form a shock wave. Optics offers an unsurpassed potential for studying the features of DSWs in repeatable lab experiments. Such experiments are accurately described by the (integrable) semiclassical nonlinear Schroedinger (NLS, also known as Gross-Pitaevskii in the context of cold atoms) equation. We review the properties of such fascinating objects in the framework of such model. Weak or strong perturbations to NLS also accounts for new phenomena such as radiation from dispersive shocks, competition of shock and other breking phenomena (modulational instability), and formation of shock from a completely random field (incoherent shock). These new directions will be also briefly discussed.
Samuel Lellouch Laboratoire Charles Fabry de l’Institut d’Optique
Collective excitations govern most dynamical properties of many-body quantum systems, such as propagation of correlations and thermalization processes. In disordered systems, the transport properties of collective excitations may however be strongly altered, mainly due to Anderson localization. The case of interacting bosons is expected to be particularly involved, since repulsive interactions in Bose systems can compete or cooperate with disorder, inducing nontrivial localization effects. In this talk, we will discuss the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid in dimension d>1. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly nonmonotonic energy dependence of the disorder parameter, which governs the localization behaviour. While in low dimensions, all excitations are localized, we find that in three dimensions, the excitation spectrum can split into alternating bands of localized and extended states, with up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.
Matteo Conforti IRCICA
Extreme wave events, such as Rogue Waves and Dispersive Shock Waves, are encountered in several physical settings, ranging from oceanography to optics, form physics of the atmosphere to Bose-Einstein condensation. I will show the development of extreme waves in different nonlinear systems, of particular relevance to nonlinear optics, such as vector NLS and three-wave interaction.
Gennady El Loughborough University
Maxime Gazeau Inria-Lille
Nous présentons un ensemble de résultats sur la dynamique spatio-temporelle des paquets d'électrons relativistes, circulant dans les anneaux de stockage (comme SOLEIL, UVSOR, etc). Lorsque la charge paquet d'électrons dépasse un certain seuil, une instabilité dynamique fait apparaitre une structure spatiale (avec une longueur d'onde de l'ordre de millimètre), pouvant évoluer de manière erratique. D'un point de vue théorique, le modèle est basé sur une équation de type Vlasov-Fokker-Planck, et l'ingrédient principal de l'instabilité est l'interaction entre les électrons. D'un point de vue expérimental, jusque récemment, les signatures de l'instabilité étaient extrêmement indirectes, et consistaient en la détection d'un rayonnement terahertz intense. Depuis 2013, il nous a été possible d'étudier de manière directe, et en temps réel, la forme des structures spatiales, avec une résolution de l'ordre de la picoseconde. Cette nouvelle possibilité permet à présent de comparer de façon extrêmement directe les résultats expérimentaux et numériques, en particulier en ce qui concerne les évolutions d! es structures spatiales en fonction du temps. Les premières observations expérimentales ont été effectuées à UVSOR (Japon, en mars 2012 et 2013), et à SOLEIL (France, en octobre-novembre 2013).
Tommaso Roscilde Laboratoire de Physique, ENS de Lyon
Miguel ONORATO (University of Turin)
P. Suret (PhLAM)
Christophe Besse (Painlevé)
Jean-Claude Garreau (PhLAM)
Stephan De Bièvre (Painlevé)