Related papers: Symmetry Breaking of Vortex Patterns in a Rotating…
We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we…
The dynamics of moving vortex lattice is considered in the framework of the time dependent Ginzburg - Landau equation neglecting effects of pinning. At high flux velocities the pinning dominated dynamics is expected to cross over into the…
Crystalline membranes are one of the rare examples of bidimensional systems in which long-range order can stabilise an ordered phase in the thermodynamic limit. By a careful analysis of the Goldstone modes counting, we propose a symmetry…
We numerically investigate a lattice regularized version of quantum electrodynamics in one spatial dimension (Schwinger model). We work at a density where lattice commensuration effects are important, and preclude analytic solution of the…
Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as…
The motion of a vortex-(anti)vortex pair is studied numerically in the framework of a dynamical Ginzburg-Landau model, relevant to the description of a superconductor or of an idealized bosonic plasma. It is shown that up to a fine…
In this note, a brief introduction to the physical and mathematical background of the two-component Ginzburg-Landau theory is given. From this theory we derive a boundary value problem whose solution can be obtained in part by solving a…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled…
We consider the linear stability to axisymmetric perturbations of the family of inviscid vortex rings discovered by Norbury (1973). Since these vortex rings are obtained as solutions to a free-boundary problem, their stability analysis is…
We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg -- Landau approach. Flux line lattice in type II superconductors undergoes a transition into three "disordered" phases: vortex…
When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu-Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges…
The article reviews recent developments on magnetic properties of superconductors with anisotropic Cooper pairing. In particular, we show how the concept of broken symmetries is applied to the investigation of the mixed state in…
We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of coherent atom-atom interaction. We find that stable vortices can be supported, and that vortex…
We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of…
We consider the Ginzburg-Landau energy $E_\epsilon$ for $\mathbb{R}^M$-valued maps defined in a cylinder shape domain $B^N\times (0,1)^n$ satisfying a degree-one vortex boundary condition on $\partial B^N\times (0,1)^n$ in dimensions $M\geq…
We derive the asymptotical dynamical law for Ginzburg-Landau vortices in an inhomogeneous background density under the Schr\"odinger dynamics, when the Ginzburg-Landau parameter goes to zero. New ingredients involve across the cores lower…
We investigate the impact of various impurities on rotating Bose-Einstein condensates confined within two-dimensional harmonic and optical lattice potentials. Without impurities, the rotating condensates display an organized square lattice…