Short range intervortex forces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911054769946624 |
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| author | Speight, Martin Winyard, Thomas |
| author_facet | Speight, Martin Winyard, Thomas |
| contents | An explicit formula for the interaction energy of $n$ vortices in the abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the interaction energy of a vortex pair with separation $d$ varies as $d^4$, not $d^2$. The formula contains $n-1$ real coefficients which are fixed by certain spectral data of the Jacobi operator of the cocentred $n$-vortex. The coefficients are computed numerically for $n=2$ and $n=3$ for couplings $0.1\leq λ\leq 2.5$. The resulting short range interaction potentials are compared with the results of full field theory simulations for $λ=0.5$ and $λ=2$, with excellent agreement at small to moderate vortex separation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short range intervortex forces Speight, Martin Winyard, Thomas High Energy Physics - Theory Superconductivity An explicit formula for the interaction energy of $n$ vortices in the abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the interaction energy of a vortex pair with separation $d$ varies as $d^4$, not $d^2$. The formula contains $n-1$ real coefficients which are fixed by certain spectral data of the Jacobi operator of the cocentred $n$-vortex. The coefficients are computed numerically for $n=2$ and $n=3$ for couplings $0.1\leq λ\leq 2.5$. The resulting short range interaction potentials are compared with the results of full field theory simulations for $λ=0.5$ and $λ=2$, with excellent agreement at small to moderate vortex separation. |
| title | Short range intervortex forces |
| topic | High Energy Physics - Theory Superconductivity |
| url | https://arxiv.org/abs/2507.10438 |