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

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.

5 pages, 8 figures

References in corpus (8)

• Emergence of turbulence in an oscillating Bose-Einstein condensate
• The critical exponents of the superfluid transition in He4
• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• Length Distributions in Loop Soups
• Percolation and coarsening in the bidimensional voter model
• Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model

Cited by in corpus (11)

• Dynamical Equilibration Across a Quenched Phase Transition in a Trapped Quantum Gas
• Kibble-Zurek Dynamics in a Trapped Ultracold Bose Gas
• Persistent current formation in double-ring geometries
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Finite temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture
• Electromagnetic Response during a Quench Dynamics to Superconducting State: Time-Dependent Ginzburg-Landau Analysis
• Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas
• Finite temperature ferromagnetic transition in coherently coupled Bose gases
• Periodic quenches across the Berezinskii-Kosterlitz-Thouless phase transition
• Equilibrium, Relaxation and Fluctuations in homogeneous Bose-Einstein Condensates: Linearized Classical Field Analysis
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model