Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Nucleation of Spontaneous Vortices in Trapped Fermi Gases Undergoing a BCS-BEC Crossover

We study the spontaneous formation of vortices during the superfluid condensation in a trapped fermionic gas subjected to a rapid thermal quench via evaporative cooling. Our work is based on the numerical solution of the time dependent crossover Ginzburg-Landau equation coupled to the heat diffusion equation. We quantify the evolution of condensate density and vortex length as a function of a crossover phase parameter from BCS to BEC. The more interesting phenomena occur somewhat nearer to the BEC regime and should be experimentally observable; during the propagation of the cold front, the increase in condensate density leads to the formation of supercurrents towards the center of the condensate as well as possible condensate volume oscillations.Comment: 5 pages, 3 figure

Nucleation-induced transition to collective motion in active systems

While the existence of polar ordered states in active systems is well established, the dynamics of the self-assembly processes are still elusive. We study a lattice gas model of self-propelled elongated particles interacting through excluded volume and alignment interactions, which shows a phase transition from an isotropic to a polar ordered state. By analyzing the ordering process we find that the transition is driven by the formation of a critical nucleation cluster and a subsequent coarsening process. Moreover, the time to establish a polar ordered state shows a power-law divergence

Spiral Motion in a Noisy Complex Ginzburg-Landau Equation

The response of spiral waves to external perturbations in a stable regime of the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It is shown that the spiral core has a finite mobility and performs Brownian motion when driven by white noise. Combined with simulation results, this suggests that defect-free and quasi-frozen states in the noiseless CGLE are unstable against free vortex excitation at any non-zero noise strength.Comment: RevTex, 4 pages, 3 figures, submitted to Phys. Rev. Let

Renormalization analysis of intermittency in two coupled maps

The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvaule associated with the scaling of the control parameter of the uncoupled one-dimensional map. However, the relevant ``coupling eigenvalue'' associated with coupling perturbation varies depending on the fixed maps. These renormalization results are also confirmed for a linearly-coupled case.Comment: 11 pages, RevTeX, 2 eps figure

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references, typos removed, accepted as Rapid Commun. in Phys. Rev.