Related papers: Nineteen vortex equations and integrability
We consider the following Chern-Simons equation, \begin{equation} \label{0.1} \Delta u+\frac 1{\varepsilon^2} e^u(1-e^u)=4\pi\sum_{i=1}^N \delta_{p_i^\varepsilon},\quad \text{in}\quad \Omega, \end{equation} where $\Omega$ is a 2-dimensional…
A characteristic property of superfluidity and -conductivity is the presence of quantized vortices in rotating systems. To study the BEC-BCS crossover the two most common methods are the Bogoliubov-De Gennes theory and the usage of an…
For $n \ge 2$, we prove that a finite volume complex hyperbolic $n$-manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of dimension at least two is arithmetic, paralleling our previous work for real…
We obtain electrically charged vortex solutions for the Born-Infeld Higgs system with a Chern Simons term. We analyse numerically these solutions, comparing their properties with those of ``normal'' Nielsen-Olesen vortices and also show…
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…
We consider relative equilibrium solutions of the two-dimensional Euler equations in which the vorticity is concentrated on a union of finite-length vortex sheets. Using methods of complex analysis, more specifically the theory of the…
We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a 2D point-like model,…
Based on the U(1) gauge potential decomposition theory and the $\phi$-mapping method, we study the vortex lines in two-gap superconductor and obtain the condition, under which the vortices can carry an arbitrary fraction of magnetic flux.…
We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the…
The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by Jackiw and Pi are generalized using the non-relativistic Kaluza-Klein-type framework…
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference…
Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler equations on 2-dimensional manifolds. Integrability results for few point-vortices on various domains is a vivid topic, with many results and…
We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex…
The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of the superfluidity of helium-four in arbitrary dimensions. The…
In this paper we establish the existence of vortex solutions for a Chern--Simons--Higgs model with gauge group $SU(N) \times U(1)$ and flavor SU(N), these symmetries ensuring the existence of genuine non-Abelian vortices through a…
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a topological/combinatorial approach following M.…
Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations.…
We derive a relationship for the vortex aspect ratio $\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies…
The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterium…
The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was…