Related papers: The Stability of Magnetic Vortices
We present for the first time solutions in the gauged $U(1)\times U(1)$ model of Witten describing vortons -- spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago,…
Since the Ginzburg-Landau theory is concerned with macroscopic phenomena, and gravity affects how objects interact at the macroscopic level. It becomes relevant to study the Ginzburg-Landau theory in curved space, that is, in the presence…
We investigate two settings of Ginzburg-Landau posed on a manifold where vortices are unstable. The first is an instability result for critical points with vortices of the Ginzburg-Landau energy posed on a simply connected, compact, closed…
Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by…
We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions.…
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge…
We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asymmetric solutions, and some of them have…
We study the long-time behaviour of helically symmetric infinite-energy solutions to the incompressible Navier-Stokes equations in the whole space $\mathbb{R}^3$. Our solutions are $H^1$-perturbations of a Lamb-Oseen vortex whose…
We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential…
The stability of an abelian (Nielsen-Olesen) vortex embedded in the electroweak theory against W production is investigated in a gauge defined by the condition of a single-component Higgs field. The model is characterized by the parameters…
We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of…
We study the stability of non-Abelian semi-local vortices based on an N=2 supersymmetric H = [SU(Nc) x U(1)]/Z_Nc = U(Nc) gauge theory with an arbitrary number of flavors (Nf > Nc) in the fundamental representation, when certain N=1 mass…
We present a discussion of embedded vortices in general Yang-Mills theories. The origin of a family structure of solutions is shown to be group theoretic in nature and a procedure for its determination is developed. Vortex stability can be…
We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found…
We study systems formed of 2N point vortices on a sphere with N vortices of strength +1 and N vortices of strength -1. In this case, the Hamiltonian is conserved by the symmetry which exchanges the positive vortices with the negative…
In this paper we prove the existence of vortices, namely standing waves with non null angular momentum, for the nonlinear Klein-Gordon equation in dimension $N\geq 3$. We show with variational methods that the existence of these kind of…
By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions…
We study the linear stability of entire radial solutions $u(re^{i\theta})=f(r)e^{i\theta}$, with positive increasing profile $f(r)$, to the anisotropic Ginzburg-Landau equation \[ -\Delta u -\delta (\partial_x+i\partial_y)^2\bar u…
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per a fundamental cell. We also revisit the existence proof for the Abrikosov vortex…
We consider the noncommutative Abelian-Higgs theory and investigate general static vortex configurations including recently found exact multi-vortex solutions. In particular, we prove that the self-dual BPS solutions cease to exist once the…