Related papers: Shape and dynamics of nonrelativistic vortex strin…
The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of…
We establish the stability of a pair of Hill's spherical vortices moving away from each other in 3D incompressible axisymmetric Euler equations without swirl. Each vortex in the pair propagates away from its odd-symmetric counterpart, while…
We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
The problem of the statistics of a set of chaotic vortex lines in a counterflowing superfluid helium is studied. We introduced a Langevin-type force into the equation of motion of the vortex line in presence of relative velocity…
The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs system is investigated from the adiabatic approach. The difficulties involved in treating the field evolution as motion on the moduli space in this system are shown.…
Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…
A homogenised model is developed to describe the interaction between aligned strings and an incompressible, viscous, Newtonian fluid. In the case of many strings, the ratio of string separation to domain width gives a small parameter which…
A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U(1)$\times$U(1) symmetric potential. Particular emphasis is given to the case, when only…
The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The…
We examine string (vortex) formation at a quench for a weakly-coupled global U(1) theory when the excitation spectrum is non-relativistic. It is so similar to vortex production in the corresponding relativistic plasma as to reinforce…
The real-time dynamics of finite-temperature gauge theories can be approximated, to leading-order accuracy in the coupling constants, by a classical field theory with the hard thermal loop Lagrangian. I show how this approach can be used in…
It has been shown recently that the motion of solitons at couplings around a critical coupling can be reduced to the dynamics of particles (the zeros of the Higgs field) on a curved manifold with potential. The curvature gives a velocity…
We propose a new Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid $^4$He. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities…
We introduce a functional framework taylored to investigate the minimality and stability properties of the Ginzburg-Landau vortex of degree one on the whole plane. We prove that a renormalized Ginzburg-Landau energy is well-defined in that…
We construct the non-relativistic parity-violating hydrodynamic description of a two-dimensional dissipative, normal fluid in presence of small U(1) background fields and vorticity. This is achieved by taking the non-relativistic limit of…
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be…
We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model.…
Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of…
We formulate non-Hermitian Landau levels in two-dimensional systems under a complex perpendicular magnetic field. In the symmetric gauge, we derive their discretely spaced, highly degenerate complex spectra and biorthogonal eigenstates, and…