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arXiv:2209.14883 · Physical Review Letters

Stable and Unstable Perturbations in Universal Scaling Phenomena Far from Equilibrium

Thimo Preis, Michał P. Heller, Jürgen Berges

Published Jan 20, 2023• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.130.031602

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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.
We compute universal scaling exponents and scaling functions for massless scalar field theories far from equilibrium. Using a large-NNN expansion to next-to-leading order, we investigate the nonperturbative infrared behaviour associated with the transport of a) energy or b) effective particle number towards low frequencies ωωω and momenta pˉ\bar ppˉ​. For massless dispersion ω=pˉω= \bar{p}ω=pˉ​, we determine the scaling form of the distribution function whose universal power-law tail fS(pˉ)∼1/pˉκf_S(\bar p) \sim 1/\bar{p}^κfS​(pˉ​)∼1/pˉ​κ is found to be a) κ=d+1κ= d+1κ=d+1 and b) κ=dκ= dκ=d in d=3d=3d=3 spatial dimensions. Our results establish that relativistic and nonrelativistic theories do not belong to the same universality class in this case, which opens up new applications to far-from-equilibrium phenomena in high-energy and (quantum) many-body physics with linear dispersions.
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Quantum many-body systems far from equilibrium can approach a nonthermal fixed point during their real-time evolution. One example is scalar field theory, which occurs in models \nof cosmological inflation, and similar examples are found for non-Abelian plasmas relevant for heavy-ion collisions and for ultracold Bose gases. Investigating nonthermal fixed points of different microscopic theories, we present two novel universality classes that provide links between these systems. \n \nOne of them involves nonrelativistic, N-component relativistic and expanding scalar systems. It occurs in the deep infrared regime of very high occupancies and is governed by a self-similar evolution. Its nonequilibrium dynamics leads to the formation of a Bose-Einstein condensate. The scaling properties of this region can be described by a vertex-resummed kinetic theory that is based on a systematic large-N expansion at next-to-leading order. \n \nThe other novel universality class encompasses scalar field theories and non-Abelian plasmas in a longitudinally expanding background and corresponds to an early dynamical stage of heavy-ion collisions in the high-energy limit. We show that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. \n \nBoth universality classes are found in separate momentum regions in a longitudinally expanding N-component scalar field theory. We argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks. Moreover, the observed universality connects different physics disciplines from heavy-ion collisions to ultracold atoms, making a remarkable link between the world's hottest and coldest matter.
We consider an effective kinetic description for quantum many-body systems, which is not based on a weak-coupling or diluteness expansion. Instead, it employs an expansion in the number of field components NNN of the underlying scalar quantum field theory. Extending previous studies, we demonstrate that the large-NNN kinetic theory at next-to-leading order is able to describe important aspects of highly occupied systems, which are beyond standard perturbative kinetic approaches. We analyze the underlying quasiparticle dynamics by computing the effective scattering matrix elements analytically and solve numerically the large-NNN kinetic equation for a highly occupied system far from equilibrium. This allows us to compute the universal scaling form of the distribution function at an infrared nonthermal fixed point within a kinetic description, and we compare to existing lattice field theory simulation results.