We examine the quantization of the motion of two charged vortices in a Ginzburg–Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac–Gupta–Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of imple...

We study the relaxation dynamics of quantum turbulence in a two-component Bose-Einstein condensate containing half-quantum vortices. find temporal scaling regime for number vortices and correlation lengths that at early times is strongly dependent on relative strength inter-species interaction. At later we becomes universal, independent interaction, approaches numerically observed scalar conden...

We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are particles subject to the mutual interaction. The dual formulation of the model is derived to explain the sign of the statistical interaction. When vortices of dif...

Chiral p-wave superconducting state supports a rich spectrum of topological excitations different from those in conventional superconducting states. Besides domain walls separating different chiral states, chiral p-wave state supports both singular and coreless vortices also interpreted as skyrmions. Here, we present a numerical study of the energetic properties of isolated singular and coreles...

Using a focused laser beam we stir a Bose-Einstein condensate confined in a magnetic trap. When the stirring frequency lies near the transverse quadrupolar mode resonance we observe the nucleation of vortices. When several vortices are nucleated, they arrange themselves in regular Abrikosov arrays, and in the limit of large quantum number the lattice structure is shown to produce a quantum velo...

Using a focused laser beam we stir a Bose-Einstein condensate confined in a magnetic trap. When the stirring frequency lies near the transverse quadrupolar mode resonance we observe the nucleation of vortices. When several vortices are nucleated, they arrange themselves in regular Abrikosov arrays, and in the limit of large quantum number the lattice structure is shown to produce a quantum velo...

Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical particles in the lowest Landau level, and vortices in the Chern-Simons Ginzburg-Landau model. In both cases the resulting classical statistical mechanics is shown t...

Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatu...

The dynamics of quantized vortices, after reconnection, is investigated within the localized induction approximation. The numerical simulations of vortex line evolution help to determine the rate of the line-length changes. In the absence of counterflow, the vortex line shortens after each reconnection and line-length reduction is calculated as a function of the friction parameter α and the rec...

We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore ...