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

¹ Department of Physics, Kyoto University - Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan
² Université Pierre et Marie Curie - Paris 6, Laboratoire de Physique Théorique et Hautes Energies - 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
³ Kavli Institute of Theoretical Physics, University of California Santa Barbara, CA 93106, USA

Received: 10 June 2016
Accepted: 28 July 2016

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 a state that is numerically indistinguishable from the one of the critical threshold, 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.