Steady-State Distributions of Interacting Discrete Vortices

Abstract

The sinh-Poisson equation describing two-dimensional steady-state distributions of elements with a logarithmic interaction potential (charged filaments executing guiding-center motion; quantized vortex lines) is solved numerically. Multiple solutions are obtained for the case of negative temperatures. These have a simple thermodynamic interpretation which agrees with the results of numerical simulations. The results are related to numerical experiments and observations of vortex filaments in liquid ${\mathrm{He}}^4$.