Long range vortex configurations in generalized models with the Maxwell or Chern-Simons dynamics

TL;DR

This paper explores vortex solutions with long-range power-law tails in generalized Maxwell-Higgs and Chern-Simons-Higgs models, deriving first order equations and revealing extended field profiles.

Contribution

It introduces a method to obtain long-range vortex solutions in both Maxwell and Chern-Simons models with generalized dynamics, including a way to match profiles across models.

Findings

Vortices with power-law tails in magnetic field and energy density.

Equivalent scalar and magnetic profiles in Maxwell and Chern-Simons models.

Potential applications to nonrelativistic systems like Rydberg atoms.

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.