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arXiv:2503.01771 · Physical Review Research

Kelvin waves in nonequilibrium universal dynamics of relativistic scalar field theories

Viktoria Noel, Thomas Gasenzer, Kirill Boguslavski

Published Jul 23, 2025• 5 citations
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Abstract

We investigate the different degrees of freedom underlying far-from-equilibrium scaling behavior in a relativistic, single-component O ( 1 ) scalar field theory in two and three spatial dimensions. In such a strongly correlated many-body system, identifying the respective roles of nonlinear wave excitations and defect dynamics is a prerequisite for understanding the universal character of time evolution far from equilibrium and thus the different possible universality classes of nonthermal fixed points. Using unequal-time two-point correlation functions, we extract information about the dominant infrared excitations and study their connections to the turbulent dynamics of topological defects created in the system. In three dimensions, the primary excitations are identified as kelvon quasiparticles, which are quantized Kelvin waves propagating along vortex lines, while in two dimensions, vortices are point defects, and the infrared dynamics is dominated by bound-state-like excitations similar to Kelvin waves. In both cases, the kelvon excitations are found to be characterized by distinct time-evolving dispersion relations, subject to the coarsening dynamics close to the respective nonthermal fixed point and, thus, to the decay of superfluid turbulence in the system. Our results underline the role of topological defects and their influence on the universal dynamics of strongly correlated systems near nonthermal fixed points, complementing the analysis of large- N models in O ( N ) systems.

DOI
10.1103/h4hn-r6kp

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Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.
Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, for example, in early universe inflation or quark-gluon plasma dynamics.
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
We study the dynamics of perturbations around nonthermal fixed points associated with universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions, we determine the stability scaling exponents using a self-consistent large-N expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasiexponential deviations from the fixed point in the infrared. We identify a tower of far-from-equilibrium quasiparticle states and their dispersion relations by computing the spectral function. With the help of linear response theory, we demonstrate that unstable dynamics arises from a competition between elastic scattering processes among the quasiparticle states. What ultimately renders the fixed point dynamically attractive is the phenomenon of a "scaling instability," which is the universal scaling of the unstable regime toward the infrared due to a self-similar quasiparticle cascade. Our results provide ab initio understanding of emergent stability properties in self-organized scaling phenomena.