Applied Mathematics Colloquium - Antiholomorphic modes in vortex lattices

Dates

Tuesday, November 22, 2022 - 14:00 to 15:00

Speaker: Thomas Machon (University of Bristol)

Abstract: Helmholtz-Kirchoff dynamics of point vortices in an ideal fluid can be used as a model of quantum vortex dynamics in superfluids. Large collections of such vortices form hexagonal lattices. Vibrational modes of these lattices were studied by Tkachenko in a series of seminal papers, so-called Tkachenko waves. We extend this analysis and show that in large but finite lattices an additional set of modes appears, described by anti-holomorphic functions and appearing as power-law confined edge modes. We show how these modes arise from a singularity of defective Hamiltonians in the Brillouin zone. Our theory is confirmed by numerical simulation.