Workshop 2025: Unveiling the Internal Structure of Topological Vortices in the Abelian-Higgs model

Session Information

Location: Lecture room F3213 - 13
Day: Wednesday, 14 May
Time: 18:00 - 19:00
Chairperson: -

Presentation Details

Presentation Type: Poster presentation
Title: Unveiling the Internal Structure of Topological Vortices in the Abelian-Higgs model
Abstract: Vortices are among the most versatile topological textures. They play a key role in diverse areas such as superconductivity, condensed matter physics, and cosmology. The most well-known model in which these solutions can be found is the Abelian-Higgs model.

Due to the relevance of this theory, it is important to understand in detail the dynamics of these objects. For example, one of the most well-known properties of these textures is the $90^\circ$ scattering that occurs when two vortices collide with the same impact velocity. It has recently been discovered that the internal mode structure associated with these solutions plays a key role in vortex dynamics, leading to fractal pattern scattering when at least one of its internal modes is initially excited.

The main goal of this talk is to study in detail the internal mode structure associated with these objects. We will show how the eigenvalue problem can be simplified by correctly choosing the angular dependence of the corresponding eigenfunctions. By doing so, the problem reduces to solving a coupled system of three second-order ordinary differential equations that can be numerically solved almost instantly.

Furthermore, we will also study the analytic properties of the eigenfunctions that solve this problem, including the behavior of these functions near the vortex center. Finally, we will analyze in detail the modes responsible for the instabilities of vortices with a topological charge greater than $n = 1$.

Presenter

Mr David Miguélez-Caballero
Department of Theoretical Physics, Atomic Physics, and Optics and Laboratory for Disruptive Interdisciplinary Science (LaDIS), University of Valladolid | Spain

Authors

1. David Miguélez-Caballero | Department of Theoretical Physics, Atomic Physics, and Optics and Laboratory for Disruptive Interdisciplinary Science (LaDIS), University of Valladolid
2. Alberto Alonso-Izquierdo | Department of Applied Mathematics and Instituto Universitario de Física Fundamental y Matemáticas, University of Salamanca
3. Jose M. Queiruga | Department of Applied Mathematics and Instituto Universitario de Física Fundamental y Matemáticas, University of Salamanca