Vortex dynamics in nonrelativistic version of Abelian Higgs model: Effects of the medium on the vortex motion

Arkadii Kozhevnikov,V.A Andrianov,V.T Kim,V.A Matveev,A.A Andrianov,M.D Fitkevich,V.A Rubakov

doi:10.1051/epjconf/201612505011

Abstract

The closed vortex dynamics is considered in the nonrelativistic version of the Abelian Higgs Model. The effect of the exchange of excitations propagating in the medium on the vortex string motion is taken into account. The obtained are the effective action and the equation of motion both including the exchange of the propagating excita- tions between the distant segments of the vortex and the possibility of its interaction with the static fermion asymmetric background. They are applied to the derivation of the time dependence of the basic geometrical contour characteristics.

Highlights

The string-like solutions of the field-theoretical models are widely discussed in application to numerous physical systems, from the really observed in condensed matter physics
The dynamics of cosmic strings was studied in the framework of the Nambu-Goto action [5] which was shown to result from the relativistic version of the Abelian Higgs model (AHM) [6]
Another limiting case is the nonrelativistic one, which can be derived from the nonrelativistic Abelian Higgs model (NRAHM)

Summary

Introduction

The string-like (or vortex) solutions of the field-theoretical models are widely discussed in application to numerous physical systems, from the really observed in condensed matter physics The solution in the form of the static cosmic string was obtained from the static version of AHM [7]. Another limiting case is the nonrelativistic one, which can be derived from the nonrelativistic Abelian Higgs model (NRAHM). The static limit of this model coincides with the Ginzburg-Landau theory [8] Another interesting aspect of the time-dependent gauge vortex solutions is that they can elucidate the interrelations among such characteristics of the closed contours as the helicity of gauge field forming the vortex, the writhe and torsion (twist) numbers and their possible dependence on time [9,10,11]. The corresponding equation of motion is obtained, side by side with expressions for the time derivatives of the curvature and torsion of the gauge vortex contour [12,13,14]

Nonrelativistic Abelian Higgs Model with the gauge vortex

Equation of the vortex motion

Time derivatives of the basic contour characteristics

Discussion and conclusion