Sergio Rica

Dynamical formation of a Bose–Einstein condensate

We explain how a condensate forms in finite time by a selfsimilar blow-up of the solution of the relevant quantum Boltzmann kinetic equation for a dilute quantum Bose gas. The condensate, once it is there, keeps exchanging mass with the rest of the distribution until equilibrium is reached, as described by a version of the kinetic equation that includes the existence of this condensate.

SPONTANEOUS CURVATURE-INDUCED PEARLING INSTABILITY

We investigate the instability of a tubular fluid membranes made of a water soluble surfactant. The tubules are obtained at high salinities. The instability is due to the introduction within the vesicle multilayer of an alkane. We measure the wavelength of this instability versus the unperturbed radius of the tubules. To interpretthis dependance we use a model that includes not only the surface tension in the elastic energy but the spontaneous curvature as well. The spontaneous curvature is induced by the presenceof the oil in the bilayer of the membrane and give a selection of a non-zero wavelength.

Wave turbulence in vibrating plates: The effect of damping

The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for increasing the dissipation are used. The main observable consequence of increasing the damping is a significant modification in the slope of the power spectral density, so that the observed power laws are not in a pure inertial regime. However, the system still displays a turbulent behavior with a cut-off frequency that is determined by the injected power which does not depend on damping. By using the measured damping power-law in numerical simulations, similar conclusions are drawn out.

Coexistence of ordinary elasticity and superfluidity in a model of a defect-free supersolid.

The mechanical behavior of a supersolid is studied in the framework of a fully explicit model derived from the Gross-Pitaevskii equation without assuming any defect or vacancy. A set of coupled nonlinear partial differential equations plus boundary conditions is derived. The conditions of mechanical equilibrium are studied under external constraints such as steady rotation and external stress. Our model explains the experimentally observed paradoxical behavior: a nonclassical rotational inertia fraction in the limit of small rotation speed but a solidlike elastic response to small stress or an external force field.

Spatio-temporal instabilities in the transverse patterns of lasers

Abstract The transverse pattern dynamics in a laser with large Fresnel number is often governed by two relatively independent but simultaneous instabilities. One, dominated by long wavelength modulations leads to a “turbulent” state (uncorrelated in space and time) principall through fluctuations of the phase of the field, while the other, which yields a periodic modulation in space and time is a Hopf bifurcation connected to the relaxation oscillation characteristics of the laser. The measured electric field amplitude is modulated by both effects. As a consequence, the laser intensity is locally chaotic on short time scales but the time-average intensity patterns retains the global symmetry of the system.

Coherence absorption and condensation induced by thermalization of incoherent nonlinear fields

We show that a conservative system of incoherent nonlinear waves exhibits, as a rule, an irreversible process of coherence transfer, in which the incoherence of the system is absorbed by the small-amplitude field, thus allowing the high-amplitude field to evolve towards a highly condensed coherent state. This process of coherence absorption results from the natural thermalization of the fields to a thermodynamic equilibrium state. The theory reveals that, contrary to a classical gas system, a wave system does not satisfy an equipartition of energy among the particles. Such a distinctive feature is the key property underlying the existence of the coherence absorption process. The coherence absorption effect is shown to also occur in a system of quantum Bose gases.

Vortex shedding in a model of superflow

The present paper represents part of the Ph.D. dissertation by C. Josserand [Dynamique des superfluides: Nucleation de vortex et transition de premier, Thesis Universite Paris VI, 1997]. We discuss the nucleation of quantized vortices in the nonlinear Schrodinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field gives an Euler‐Tricomi type equation for the stationary solutions below threshold. This equation is closely related to the one known in shock wave dynamics for gas. Then using the solvability condition, we extract a time-dependent scenario for the evolution of the amplitude of the solution, which we, finally, relate to a known family solution of NLS which gives rise to a vortex nucleation. We also give a first order correction at the Landau velocity of nucleation, taking into account the geometry of the flow. ©1999 Elsevier Science B.V. All rights reserved.

Self-Organized Societies

We characterize the behavior and the social structures appearing from a model of general social interaction proposed by Sakoda. The model consists of two interacting populations in a two-dimensional periodic lattice with empty sites. It contemplates a set of simple rules that combine attitudes, ranges of interactions, and movement decisions. We analyze the evolution of the 45 different interaction rules via a Potts-like energy function which drives the system irreversibly to an equilibrium or a steady state. We discuss the robustness of the social structures, dynamical behaviors, and the existence of spatial long range order in terms of the social interactions and the equilibrium energy.

Impurity crystal in a bose-einstein condensate.

We investigate the behavior of impurity fields immersed in a larger condensate field in various dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive condensate-mediated interaction between two impurities. Generalizing the analysis to N impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity; i.e., the system can be seen to exhibit supersolid behavior.

Déformation des coques élastiques

Resume Nous etudions le contact d’une coque elastique avec un plan rigide. L’experience montre une transition du premier ordre entre deux configurations differentes: la premiere est caracterisee par un contact total entre coque et plan; dans la seconde la coque se renverse en creant un creux. Nous discutons les energies de chaque configuration pour expliquer la transition observee.