Compact Vortices

TL;DR

This paper explores generalized Maxwell-Higgs models with variable magnetic permeability to construct and analyze compact vortex solutions, including their properties, energy density, and magnetic field profiles, through asymptotic analysis and numerical methods.

Contribution

It introduces new models with generalized permeability that enable the construction of compact vortices, expanding the understanding of vortex configurations in gauge field theories.

Findings

Development of models with distinct permeability profiles

Numerical solutions demonstrating compact vortex configurations

Analysis of energy density and magnetic field behavior

Abstract

We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane.