涡旋与因式分解

Nineteen vortex equations and integrability

The class of five integrable vortex equations discussed recently by Manton is extended so it includes the relativistic BPS Chern-Simons vortices, yielding a total of nineteen vortex equations. Not all the nineteen vortex equations are integrable, but four new integrable equations are discovered and we generalize them to infinitely many sets of four integrable vortex equations, with each set denoted by its integer order $n$. Their integrability is similar to the known cases, but give rise to different (generalized) Baptista geometries, where the Baptista metric is a conformal rescaling of the b…

Exotic vortices and twisted holomorphic maps

We consider the exotic vortex equations on compact Riemann surfaces. These generalise the well-known Jackiw-Pi and Ambjørn-Olesen vortex equations and arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in nonrelativistic Chern-Simons-matter theories. We show that (exotic) vortex solutions in $U(N)$ gauge theories with a single fundamental flavour on compact Riemann surfaces can be constructed from gauged holomorphic maps into complex space forms of dimension $N$. We conjecture, with some evidence, that all such solutions arise this way. This leads us to insights regarding …

Generating Functions, Polynomials and Vortices with Alternating Signs in Bose-Einstein Condensates

In this work, we construct suitable generating functions for vortices of alternating signs in the realm of Bose-Einstein condensates. In addition to the vortex-vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we reconstruct collinear few-vortex equilibria obtained in earlier work, as well as extend them to larger numb…

Dynamical aspects of a restricted three-vortex problem

The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with non-zero circulation remains stationary. By using the basic dynamical system theory, it is shown that the vortex motion is always bounded and any configuration of vortices must go through at least one collinear state. The present analysis reveals that the inter-vortex distances in any non-fixed configuration of vortices are either periodic in time or aperiodic…

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

修正的阿贝尔-希格斯模型中的涡旋团与充满涡旋的气泡

Vortex clusters and vortex-filled bubbles in a modified Abelian-Higgs model

研究具有八阶标量势的修正阿贝尔-希格斯模型，发现其存在类1.5型涡旋行为，解析构造畴壁并分析涡旋相互作用与多涡旋分裂不稳定性，揭示涡旋团与充满涡旋气泡的形成机制。