Cherenkov radiation from an Abrikosov-Josephson vortex

The Cherenkov radiation of generalized Swihart waves is investigated in connection with the slow motion of an Abrikosov-Josephson vortex, which corresponds to a 2 π kink in the phase difference of Cooper pairs on opposite sides of a tunnel junction. The radiative friction force acting on such a vortex is determined. An evaluation is made of the steady-state vortex velocity when the accelerating influence of an electric current through the Josephson junction is compensated by radiative slowing of the vortex due to Cherenkov radiation from the Abrikosov-Josephson vortex. Fiz. Tverd. Tela (St. Petersburg) 39, 444–448 (March 1997)     

Finite number of vortices and bending of finite vortex lines in a confined rotating Bose-Einstein condensate

The minimal energy configurations of finite N_v-body vortices in a rotating trapped Bose-Einstein condensate is studied analytically by extending the previous work [Y. Castin, R. Dum, Eur. Phys. J. D 7, 399 (1999)], and taking into account the finite size effects on z-direction and the bending of finite vortex lines. The calculation of the energy of the vortices as a function of the rotation frequency of the trap gives number, curvature, configuration of vortices and width of vortex cores self-consistently. The numerical results show that (1) the simplest regular polynomial of the several vortex configurations is energetically favored; while the hexagonal vortex lattice is more stable than square lattice; (2) bending is more stable then straight vortex line along the z-axis for λ<1; (3) the boundary effect is obvious: compared with the estimation made under infinite boundary, the finite size effect leads to a lower vortex density, while the adding vortex bending results in a less higher density because of the expansion. The results are in well agreement with the other authors' ones.     

Cherenkov interaction of vortices with a free surface

The interaction of vortex filaments in an ideal incompressible fluid with the free surface of the latter is investigated in the canonical formalism. A Hamiltonian formulation of the equations of motion is given in terms of both canonical and noncanonical Poisson brackets. The relationship between these two approaches is analyzed. The Lagrangian of the system and the Poisson brackets are obtained in terms of vortex lines, making it possible to study the dynamics of thin vortex filaments with allowance for finite thickness of the filaments. For two-dimensional flows exact equations of motion describing the interaction of point vortices and surface waves are derived by transformation to conformal variables. Asymptotic steady-state solutions are found for a vortex moving at a velocity lower than the minimum phase velocity of surface waves. It is found that discrete coupled states of surface waves above a vortex are possible by virtue of the inhomogeneous Doppler effect. At velocities higher than the minimum phase velocity the buoyant rise of a vortex as a result of Cherenkov radiation is described in the semiclassical limit. The instability of a vortex filament against three-dimensional kink perturbations due to interaction with the “image” vortex is demonstrated. Zh. éksp. Teor. Fiz. 115, 894–919 (March 1999)     

Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices

We study the Abelian Higgs vortex solutions to the sinh-Gordon equation and the elliptic Tzitzeica equation. Starting from these particular vortices, we construct solutions to the Taubes equation with higher vortex number, on surfaces with conical singularities.We then, analyse more general properties of vortices on such singular surfaces and propose a method to obtain vortices on conifolds from vortices on surfaces of revolution. We apply our method to construct explicit vortex solutions on the Poincaré disk with a conical singularity in the centre, to which we refer as the “hyperbolic cone”.We uplift the Abelian sinh-Gordon and Tzitzeica vortex solutions to four dimensions and construct cylindrically symmetric, self-dual Yang–Mills instantons on a non-self-dual (nor anti-self-dual) 4-dimensional Kähler manifold with non-vanishing scalar curvature. The instantons we construct in this way cannot be obtained via a twistorial approach.     

Poisson bracket scheme for vortex dynamics in superfluids and superconductors and the effect of the band structure of the crystal

Poisson brackets for the Hamiltonian dynamics of vortices are discussed for 3 regimes, in which the dissipation can be neglected and the vortex dynamics is reversible: (i) The superclean regime, in which the spectral flow is suppressed. (ii) The regime in which the fermions are pinned by the crystal lattice. This includes the regime of extreme spectral flow of fermions in the vortex core: these fermions are effectively pinned by the normal component. (iii) The case when the vortices are strongly pinned by the normal component. All these limits are described by the single parameter C ₀, the physical meaning of which is discussed for superconductors containing several bands of electrons and holes. The effect of the topology of the Fermi surface on the vortex dynamics is also discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 794–800 (10 December 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Monopole and vortex dissociation and decay of the false vacuum

If monopole (or vortex) solutions exist for a metastable or false vacuum, a finite density of monopoles (or vortices) can act as impurity sites that trigger inhomogeneous nucleation and decay of the false vacuum. The monopoles (or vortices) become classically unstable and their cores expand radially, converting the volume of the system to the phase represented by the core of the monopole (or vortex). False vacuum decay about the monopole (or vortex) sites occurs for values of the barrier height and energy difference between the true and false phases that are insufficient for homogeneous bubble nucleation. Two cases where the phenomenon may play a role are phase transitions in early cosmology and in ³H-⁴He mixtures at low temperatures.     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Magnetic vortices and thermoelectric effect in a hollow superconducting cylinder

The question of a surface barrier which determines the behavior of a vortex in a hollow superconducting cylinder of finite thickness in an external magnetic field is discussed, taking into account magnetic flux quantization in the cavity. The behavior of magnetic vortices in a hollow superconductor in the presence of a thermoelectric current is also considered. Pairs of magnetic vortices with opposite magnetic field orientations (vortex-antivortex pairs) are generated by this current near T _c. The thermoelectric current drives the antivortex (the vortex with oppositely directed field) out of the cylinder, whereas the vortex is ejected into the cavity and remains on the inside cylinder surface as a current. The number of magnetic flux quanta trapped inside the cylinder increases by one. The relation of this mechanism to the “giant” thermoelectric effect in hollow superconductors is discussed. Zh. éksp. Teor. Fiz. 111, 2175–2193 (June 1997)     

Vortex states in antiferromagnetic crystals

It is shown that axially symmetric two-dimensional nonuniform states can exist in easy-axis and cubic antiferromagnets lacking inversion symmetry, in the form of two-dimensional spatially modulated structures (magnetic vortex lattices) and isolated two-dimensional structures (vortices). The structure and equilibrium dimensions of the lattices and vortices have been determined by numerical solution of differential equations. Fiz. Tverd. Tela (St. Petersburg) 40, 1486–1493 (August 1998)     

Fermion zero modes in the presence of non-abelian vortices

The Dirac equation in the presence of non-abelian vortices is investigated . For isospinor fermions coupled to the vortex in the SU(2) Nielsen-Olesen model, there are normalisable well-behaved zero-energy solutions. When the fermions are in the adjoint representation there are no normalisable zero modes. The Z₂ vortex appearing in a SO(10) theory is explicitly constructed and it is shown that the heavy neutrino can be bound to it in a zero-energy state.     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

Non-Abrikosov vortices in liquid metallic hydrogen

We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg–Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet (D)-type and Gross–Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magnetic field. The presence of such a vortex is related to metallic superfluid state suggested by Babaev (2004) [1].     

High precision solutions to quantized vortices within Gross–Pitaevskii equation

The dynamics of vortices in Bose–Einstein condensates of dilute cold atoms can be well formulated by Gross–Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential equation for the vortex to very high precision is proposed. Through two-point Padé approximants, these solutions are presented in terms of simple rational functions, which can be used in the simulation of vortex dynamics. The precision of the solutions is sensitive to the connecting parameter and the truncation orders. It can be improved significantly with a reasonable extension in the order of rational functions. The errors of the solutions and the limitation of two-point Padé approximants are discussed. This investigation may shed light on the exact solution to the nonlinear vortex equation.     

Pinning of planar vortices and magnetic field penetration in a three-dimensional Josephson medium

The behavior of planar (laminar) vortices in a three-dimensional, ordered Josephson medium as a function of the parameter I, which is proportional to the critical junction current and the cell size, is investigated with allowance for pinning due to the cellular structure of the medium. The minimum possible distances between two isolated vortices are calculated. A system of vortices formed in a sample in a monotonically increasing external magnetic field is analyzed. The minimum distance from the outermost vortex to the nearest neighbor is proportional to I ^−1.1. For I⩽1.3 each vortex contains a single flux quantum Φ₀, and the distance between them does not decrease in closer proximity to the boundary but remains approximately constant, implying that the magnetic field does not depend on the coordinate in the region penetrated by vortices. These facts contradict the generally accepted Bean model. The sample magnetization curve has a form typical of type II superconductors. Allowance for pinning raises the critical field H _c and induces a sudden jump in the curve at H=H _c. Zh. Tekh. Fiz. 67, 38–46 (September 1997)     

双层量子霍尔系统在填充因子υ=1/2态的涡流解(英文)

以双层系统的ZHK 模型为基础,研究了双层量子霍尔系统在朗道填充因子取υ = 1=2 这种状态的静态涡流解。ZHK模型是一种包含Chern-Simons 规范相互作用的有效理论。为了简便,假定涡流具有柱对称的结构,随后写出了无量纲的非线性运动方程组,并分析了解的渐进行为。另外,在自对偶条件下,确定了自耦合常数的形式,并写出了关于密度的自对偶方程。最后,使用数值方法找到了类型分别为(0,1),(0, -1),(1,-1) 和(-1,-1) 的涡流解。发现拓扑数为(1,-1) 的涡流是不稳定的,它会衰变为(1,0) 和(0,-1) 两种涡流。数值结果表明,拓扑数为(0,-1)和(-1,-1)的涡流确实是自对偶涡流解。We investigate the static vortex solutions of a bilayer quantum Hall state at the Landau-level filling factor υ = 1=2. This work is based on the ZHK model, which is an effective field theory including Chern-Simons gauge interactions. We deduce the dimensionless nonlinear equations of motion for vortices possessing cylindrically symmetry, and analyze the asymptotical behaviors of solutions. Additionally, we analyze the values of critical coupling constants under the self-dual condition, and obtain the self-dual equations. Finally, vortices of type (0,1),(0, -1),(1,-1) and (-1,-1) are solved with numerical methods. We reach the conclusion that vortex of type (11,-1) is unstable, which will decay to (1,0) and (0,-1). The vortices of type (0,-1) and (-1,-1) are self-dual solutions from numerical results.     

New omega vortex identification method

A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.     

Influence of orbital motion on the collapse of ring vortices in an accretion flow

The orbital motion along the directrix of ring vortices (vortex with swirl) regulated by helicity can exert a significant influence on the vortex collapse and motion in a convergent (accretion) flow. The solutions for both single and dipole toroidal vortices in Hamiltonian representation have been obtained. The phenomenon considered can have applications in the astrophysics of active galactic nuclei and the dynamics of atmospheric vortices.     

Metastability and vortex pairing in the kolmogorov flow

We show that a system of very elongated vortices, such as appear in the Kolmogorov flow near threshold can go through a succession of quasi-equilibrium vortex solutions with n, n−1, n−2, … vortices. The result applies more generally to the competition between cellular solutions in “zig-zag” instabilities.