相关论文: Are Vortex Numbers Preserved?
Topological excitations are believed to play an important role in different areas of physics. For example, one case of topical interest is the use of dual models of quantum cromodynamics to understand properties of its vacuum and…
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; it can therefore be interpreted as a spinning bubble of air in water. This paper gives a general method for desingularizing…
Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The distinctive feature of a non-Abelian vortex is the presence of an internal CP^{N-1}…
In a previous work (arXiv:2306.05948), we constructed by convex integration examples of energy dissipating solutions to the 2D Euler equations on $\mathbb{R}^2$ with vorticity in the real Hardy space $H^p(\mathbb{R}^2)$. In the present…
In the framework of 2D ideal Hydrodynamics a vortex system is defined as a smooth vorticity function having few positive local maxima and negative local minima separated by curves of zero vorticity. Invariants of such structures are…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
I show the existence of a new type of vortex solution which is non-static but stationary and carries angular momentum. This {\it spinning vortex} can be embedded in models with trivial vacuum topology like a model with $SU(2)_{global}\times…
A numerical search for straight superconducting vortices in a U(1) model with a Ginzburg-Landau potential containing a cubic term, is presented. Such vortices exist in a small numerically determined region. The reasons of their existence in…
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 construct algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally invariant and equivalent to noncommutative algebra of canonical type. Influence of noncommutativity on the energy levels of…
Quantized vortices have been observed in a variety of superfluid systems, from $^4$He to condensates of alkali-metal bosons and ultracold Fermi gases along the BEC-BCS crossover. In this article we study the stability of singly quantized…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
The interaction of a magnetic flux vortex with weak external fields is considered in the framework of the Abelian Higgs model. The approach is based on the calculation of the zero-mode excitation probability in the external field. The…
We consider density solutions for gradient flow equations of the form $u_t = \nabla \cdot ( \gamma(u) \nabla \mathrm N(u))$, where $\mathrm N$ is the Newtonian repulsive potential in the whole space $\mathbb R^d$ with the nonlinear convex…
We investigate canonical structure of the Abelian Higgs model within the framework of DLCQ. Careful boundary analysis of differential equations, such as the Euler-Lagrange equations, leads us to a novel situation where the canonical…
This paper analyzes the space of steady rotating solutions to the two-dimensional incompressible Euler equations nearby vortex patch solutions satisfying a natural nondegeneracy condition. We address the question of desingularization and…
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…
This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the…
For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…