Chiral edge modes in Helmholtz-Onsager vortex systems

Abstract

Vortices play a fundamental role in the physics of two-dimensional (2D) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, point vortices in a 2D fluid continue to pose interesting theoretical problems, owing to their unusual statistical mechanics. Here we show that the strongly interacting Helmholtz-Onsager vortex systems can form statistical edge modes at low energies, extending a previously identified analogy between vortex matter and quantum Hall systems. Through dynamical simulations, Monte-Carlo sampling, and mean-field theory, we demonstrate that these edge modes are associated with the formation of dipoles of real and image vortices at boundaries. The edge modes are robust, persisting in nonconvex domains, and are in quantitative agreement with the mean-field predictions.

Axis-symmetric Onsager clustered states of point vortices in a bounded domain

“…Note that in some literature, Eq. ( 53) does not have the prefactor 4π and hence the solution looks slightly different [35,45]. Distinct from Eq.…”

Anti-holomorphic modes in vortex lattices

“…We also do not see the filamentation observed in the continuum system [37], whether this effect can be explicitly derived in a fully non-linear theory remains an interesting topic for future study. We note that there has been related work on statistical edge modes [38], exploiting the anomalous statistical mechanics of vortices [39]. The modes we describe are reminiscent of conformal crystals, numerically observed in vortex lattices in superconductors [40].…”

Surface waves and bulk Ruderman mode of a bosonic superfluid vortex crystal in the lowest Landau level

“…Substituting now the expressions (22) with n = 0 into this equation, we obtain the condition J 2 (kR) = 0. This gives rise to the following quantization of momenta…”

“…These studies analyze rotating superfluids in the incompressible regime, where vortices interact with each other through a logarithmic two-body interaction. In this regime, edge waves of different types were identified and recently investigated in [20][21][22][23]. Beyond the incompressible limit, the edge collective modes of arrays of vortices in superfluids have been analyzed previously in [24].…”