Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds

Badal R, Cicalese M (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Book Volume: 64

Article Number: 83

Journal Issue: 3

DOI: 10.1007/s00526-024-02886-3

Abstract

On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg–Landau and a perimeter term. Our scaling allows low-energy states to be described by an order parameter which can have finitely many point singularities (vortex-like defects) of (possibly) fractional-degree connected by line discontinuities (string defects) of finite length. Our main result is a compactness and Γ-convergence theorem which shows how the coarse grained limit energy depends on the geometry of the manifold in driving the interaction between vortices and string defects.

Authors with CRIS profile

Rufat Badal Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Badal, R., & Cicalese, M. (2025). Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds. Calculus of Variations and Partial Differential Equations, 64(3). https://doi.org/10.1007/s00526-024-02886-3

MLA:

Badal, Rufat, and Marco Cicalese. "Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds." Calculus of Variations and Partial Differential Equations 64.3 (2025).

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