Miguel Hoyuelos

Dynamics of defects in the vector complex Ginzburg-Landau equation

Abstract Coupled Ginzburg–Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special symmetries and can be written as a vector complex Ginzburg-Landau (CGL) equation . Dynamical properties of localized structures of topological character in this vector-field case are considered. Creation and annihilation processes of different kinds of vector defects are described, and some of them interpreted in theoretical terms. A transition between different regimes of spatiotemporal dynamics is described.

SPATIOTEMPORAL CHAOS, LOCALIZED STRUCTURES AND SYNCHRONIZATION IN THE VECTOR COMPLEX GINZBURG LANDAU EQUATION

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg–Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.

Defect-freezing and defect-unbinding in the Vector Complex Ginzburg-Landau equation

Abstract We describe the dynamical behavior found in numerical solutions of the Vector Complex Ginzburg–Landau equation in parameter values where plane waves are stable. Topological defects in the system are responsible for a rich behavior. At low coupling between the vector components, a frozen phase is found, whereas a gas-like phase appears at higher coupling. The transition is a consequence of a defect unbinding phenomena. Entropy functions display a characteristic behavior around the transition.

Quantum statistics of classical particles derived from the condition of free diffusion coefficient

We derive an equation for the current of particles in energy space; particles are subject to a mean-field effective potential that may represent quantum effects. From the assumption that noninteracting particles imply a free diffusion coefficient in energy space, we derive Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. Other new statistics are associated to a free diffusion coefficient; their thermodynamic properties are analyzed using the grand partition function. A negative relation between pressure and energy density for low temperatures can be derived, suggesting a possible connection with cosmological dark energy models.

Transport of interacting particles in a chain of cavities: description through a modified Fick-Jacobs equation.

We study the transport process of interacting Brownian particles in a tube of varying cross section. To describe this process we introduce a modified Fick-Jacobs equation, considering particles that interact through a hard-core potential. We were able to solve the equation with numerical methods for the case of symmetric and asymmetric cavities. We focused in the concentration of particles along the direction of the tube. We also preformed Monte Carlo simulations to evaluate the accuracy of the results, obtaining good agreement between theory and simulations.

Current of interacting particles inside a channel of exponential cavities: Application of a modified Fick-Jacobs equation.

Recently a nonlinear Fick-Jacobs equation has been proposed for the description of transport and diffusion of particles interacting through a hard-core potential in tubes or channels of varying cross section [Suárez et al., Phys. Rev. E 91, 012135 (2015)]PLEEE81539-375510.1103/PhysRevE.91.012135. Here we focus on the analysis of the current and mobility when the channel is composed by a chain of asymmetric cavities and a force is applied in one or the opposite direction, for both interacting and noninteracting particles, and compare analytical and Monte Carlo simulation results. We consider a cavity with a shape given by exponential functions; the linear Fick-Jacobs equation for noninteracting particles can be exactly solved in this case. The results of the current difference (when a force is applied in opposite directions) are more accurate for the modified Fick-Jacobs equation for particles with hard-core interaction than for noninteracting ones.

From hexagons to optical turbulence

Summary form only given. The transition from regular static patterns observed in optical systems to spatio-temporal chaotic regimes is not yet well understood. We address this problem in a ring cavity filled with a nonlinear self-focusing Kerr medium pumped by an external field. In the mean-field approximation the transverse dynamics of the slowly varying electric field amplitude E is governed by a driven-damped nonlinear Schroedinger equation.

Polarization Patterns in Kerr Media

We study spatiotemporal pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a Kerr medium in a cavity with flat mirrors and driven by a coherent plane-wave field. We consider linearly as well as elliptically polarized driving fields, and situations of self-focusing and self-defocusing. For the case of self-defocusing and a linearly polarized driving field, there is a stripe pattern orthogonally polarized to the driving field. Such a pattern changes into a hexagonal pattern for an elliptically polarized driving field. The range of driving intensities for which the pattern is formed shrinks to zero with increasing ellipticity. For the case of self-focusing, changing the driving field ellipticity leads from a linearly polarized hexagonal pattern ~for linearly polarized driving! to a circularly polarized hexagonal pattern ~for circularly polarized driving!. Intermediate situations include a modified Hopf bifurcation at a finite wave number, leading to a time dependent pattern of deformed hexagons and a codimension 2 Turing-Hopf instability resulting in an elliptically polarized stationary hexagonal pattern. Our numerical observations of different spatiotemporal structures are described by appropriate model and amplitude equations. @S1063-651X~98!12608-9#