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Anti-Holomorphic Modes in Vortex Lattices
by Brook J Hocking, Thomas Machon
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Thomas Machon |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202207_00001v2 (pdf) |
| Date accepted: | Jan. 10, 2023 |
| Date submitted: | Nov. 20, 2022, 4:57 p.m. |
| Submitted by: | Thomas Machon |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.
Published as SciPost Phys. 14, 080 (2023)