Related papers: Quasi-compact vortices
Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group $G=U(1)\times SU(N)$ and with $N$…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
Magnetic fluids are colloidal suspensions of ferromagnetic particles covered with a surfactant layer, dispersed in a host liquid. The existence of cooperative phenomena in such magnetic colloidal systems, makes the determining of their…
We study the spin vortices and skyrmions coherently imprinted into an exciton-polariton condensate on a planar semiconductor microcavity. We demonstrate that the presence of a polarization anisotropy can induce a complex dynamics of these…
An existence theory is established for a coupled non-linear elliptic system, known as "vortex equations", describing the fractional quantum Hall effect in 2-dimensional double-layered electron systems. Via variational methods, we prove the…
I discuss in these lectures vortex-like classical solutions to the equations of motion of gauge theories with spontaneous symmetry breaking. Starting from the Nielsen-Olesen ansatz for the Abelian Higgs model, extensions to the case in…
We theoretically study physical properties of the low-energy quasiparticle excitations at the vortex core in the full-gap superconducting state of the Kondo lattice coupled to compensated metals. Based on the mean-field description of the…
We study vortex solutions in the Born-Infeld theory coupled with a complex scalar field. We show that for a specific form of the "Higgs" potential the vortex satisfies a set of Bogomol'nyi-type equations. Another model, with nonlinear…
The influence of the geometry of a thin superconducting sample on the penetration of the magnetic field lines and the arrangement of vortices are investigated theoretically. We compare superconducting disks, squares and triangles with the…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
Recent experiments on mesoscopic samples and theoretical considerations lead us to analyze multiply charged ($n>1$) vortex solutions of the Ginzburg-Landau equations for arbitrary values of the Landau-Ginzburg parameter $\kappa$. For $n\gg…
The Taubes equation for Abelian Higgs vortices is generalised to five distinct U(1) vortex equations. These include the Popov and Jackiw--Pi vortex equations, and two new equations. The Baptista metric, a conformal rescaling of the…
We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices form a Hamiltonian system that conserves total dipole moment and trace of the quadrupole moment of vorticity; thereby…
It is known that, in continuous media, composite solitons with hidden vorticity, which are built of two mutually symmetric vortical components whose total angular momentum is zero, may be stable while their counterparts with explicit…
We study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the winding number of a vortex is naturally extended…
It is shown that the order parameter $\Delta$ induced in the normal part of superconductor-normal-superconductor proximity system is modulated in the magnetic field differently from vortices in bulk superconductors. Whereas $\Delta$ turns…
We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\propto r^k$ can be…
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…