KIP publications

year 2022
author(s) Philipp Heinen, Aleksandr N. Mikheev, Christian-Marcel Schmied and Thomas Gasenzer
title Non-thermal fixed points of universal sine-Gordon coarsening dynamics
KIP-Nummer HD-KIP 22-67
KIP-Gruppe(n) F27
document type Paper
source arXiv:2212.01162 [cond-mat.quant-gas]
doi 10.48550/arXiv.2212.01162
Abstract (en)

We examine coarsening of field-excitation patterns of the sine-Gordon (SG) model, in two and three spatial dimensions, identifying it as universal dynamics near non-thermal fixed points. The SG model is relevant in many different contexts, from solitons in quantum fluids to structure formation in the universe. The coarsening process entails anomalously slow self-similar transport of the spectral distribution of excitations towards low energies, induced by the collisional interactions between the field modes. The focus is set on the non-relativistic limit exhibiting particle excitations only, governed by a Schrödinger-type equation with Bessel-function non-linearity. The results of our classical statistical simulations suggest that, in contrast to wave turbulent cascades, in which the transport is local in momentum space, the coarsening is dominated by rather non-local processes corresponding to a spatial containment in position space. The scaling analysis of a kinetic equation obtained with path-integral techniques corroborates this numerical observation and suggests that the non-locality is directly related to the slowness of the scaling in space and time. Our methods, which we expect to be applicable to more general types of models, could open a long-sought path to analytically describing universality classes behind domain coarsening and phase-ordering kinetics from first principles, which are usually modelled in a near-equilibrium setting by a phenomenological diffusion-type equation in combination with conservation laws.

  author   = {Heinen, Philipp and Mikheev, Aleksandr N. and Schmied, Christian-Marcel and Gasenzer, Thomas},
  title    = {Non-thermal fixed points of universal sine-Gordon coarsening dynamics},
  journal  = {},
  year     = {2022},
  month    = {12},
  doi      = {10.48550/arXiv.2212.01162}
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