Planar ringlike vortices

Abstract

We investigate the presence of vortex structures in generalized Maxwell-Higgs and Chern-Simons-Higgs models in the three-dimensional spacetime. Despite the important difference between the Maxwell and Chern-Simons dynamics, we have been able to introduce first order differential equations that solve the equations of motion for static and rotationally symmetric field configurations. In both cases, solutions of the first order equations engender minimum energy, and we have found vortex configurations whose internal structure unveils interesting and unusual ringlike profile.

Multilayered vortices

“…This is harder because the Chern-Simons vortex is charged electrically, engendering a constraint that must be solved appropriately to generate acceptable solution. However, a Chern-Simons model was investigated recently in [24] and the results motivate further investigation on this issue.…”

“…The above field configurations are invariant under rotations in the plane, and one may follow the lines of Ref. [17,24] to find a first order framework that minimizes the energy of our system. It arises with the potential…”

Electrically charged localized structures

“…The use of a field-dependent function coupled with the gauge field dynamical term has also been recently considered in [14] in the electric context, that is, in the presence of an electric charge fixed at the origin; there, we showed that the electric field has a behavior that captures the basic feature of asymptotic freedom, an effect that is usually associated to quarks and gluons. It was also considered, for instance, in [15][16][17][18][19] to describe vortex configurations with internal structures in the plane in the magnetic context. Moreover, very recently, in [20] the authors studied the dielectric Skyrme model, that is, the Skyrme model where both the kinetic and Skyrme terms are multiplied by field-dependent functions, leading to new results of current interest.…”

“…The field-dependent function can be used to modify the magnetic properties of the medium to study vortices, as in [7][8][9][15][16][17][18][19], but it can also be considered to modify electrical properties of the medium, as in [3,4] and in [14], for instance.…”

Quasi-compact vortices

“…Due to the form of the first order equations Eq. (24) and (25), the peak of the magnetic field appears when g(r) attains a value that is the maximum point of the potential in |ϕ| ∈ [0, 1]. The energy density comes from Eq.…”