Abstract
In this work we deal with vortices in Maxwell-Higgs or Chern-Simons-Higgs models that engender long range tails. We find first order differential equations that support minimum energy solutions which solve the equations of motion. In the Maxwell scenario, we work with generalised magnetic permeabilities that lead to vortices described by solutions, magnetic field and energy density with power-law tails that extend farther than the standard exponential ones. We also find a manner to obtain a Chern-Simons model with the same scalar and magnetic field profiles of the Maxwell case. By doing so, we also find vortices with the aforementioned long range feature, which is also present in the electric field in the Chern-Simons model. The present results may motivate investigations on nonrelativistic models, in particular in the case involving Rydberg atoms, which are known to present long range interactions and relatively long lifetimes.
Highlights
In high-energy physics, vortices are planar structures that appear under the action of a complex scalar field coupled to a gauge field under an Uð1Þ local symmetry [1,2]
Before going further, we review the asymptotic behavior of the standard vortex (μ 1⁄4 1), which is described by the first-order equations and we must solve the equations in Eq (11), which become g0 1⁄4 ag and − a0 1⁄4 2sg2s−2ð1 − g2sÞ1þ1s: ð18Þ
We have investigated the presence of vortices with a long range behavior in Maxwell-Higgs and Chern-Simons-Higgs models
Summary
In high-energy physics, vortices are planar structures that appear under the action of a complex scalar field coupled to a gauge field under an Uð1Þ local symmetry [1,2]. We emphasize that the presence of vortices with long range tails in high-energy physics may trigger further interest on this kind of configuration, since the distinct tail may modify the way they interact with one another, leading to a novel collective behavior. This is the main motivation of this work, and we think it can attract interest to nonrelativistic models, in particular, to the case of the GrossPitaevskii equation, which is appropriate to describe vortex excitations in Bose-Einstein condensates [30,31]. Another possibility concerns the study of cold and ultracold hybrid ion-atom systems [34]
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