Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle

Abstract

We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II su- perconductors, magnetic materials and aspects of cosmology. We characterise the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully-packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls-off algebraically and we associate it to a geometric percolation transition that we characterise in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermo- dynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach towards a state that, within numerical accuracy, shares many features with the one at the percolation threshold, a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops, and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length-scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.

81 pages, 40 figures

References in corpus (13)

• The critical exponents of the superfluid transition in He4
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Quantum and quasiclassical types of superfluid turbulence
• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Non-equilibrium relaxation of an elastic string in a random potential
• Growing correlations and aging of an elastic line in a random potential
• Geometric properties of two-dimensional coarsening with weak disorder
• Geometry and scaling of tangled vortex lines in three-dimensional random wave fields
• Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model
• Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics
• Phase separation and critical percolation in bidimensional spin-exchange models
• Nonequilibrium critical dynamics of the three-dimensional gauge glass

Cited by in corpus (4)

• Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas
• Coexistence of defect morphologies in three dimensional active nematics
• Dynamics of topological defects after a photo-induced melting of a charge-density wave
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model