Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network

TL;DR

This paper investigates the evolution and morphology of vortex networks in 3D weakly interacting bosons using the stochastic Gross-Pitaevskii equation, revealing a percolation transition and fractal properties of vortex loops.

Contribution

It provides a detailed characterization of vortex network dynamics and morphology during thermal quenches, including the identification of a percolation transition in out-of-equilibrium conditions.

Findings

Vortex filament statistics match fully-packed loop models at high temperature.

A geometric percolation transition occurs within the ordered phase.

Long vortex loops maintain fractal properties during coarsening.

Abstract

We study the evolution of 3d weakly interacting bosons at finite chemical potential with the stochastic Gross-Pitaevskii equation. We fully characterise the vortex network in an out of equilibrium. At high temperature the filament statistics are the ones of fully-packed loop models. The vortex tangle undergoes a geometric percolation transition within the thermodynamically ordered phase. After infinitely fast quenches across the thermodynamic critical point deep into the ordered phase, we identify a first approach towards the critical percolation state, a later coarsening process that does not alter the fractal properties of the long vortex loops, and a final approach to equilibrium. Our results are also relevant to the statistics of linear defects in type II superconductors, magnetic materials and cosmological models.