Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes

Orioli, Asier Piñeiro; Berges, Jürgen

doi:10.1103/physrevlett.122.150401

Cited by 22 publications

(25 citation statements)

References 25 publications

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“…To learn more about soft dynamics, further numerical studies are required. These include also unequal-time correlators that can be studied numerically with methods that have been developed recently [41] and successfully used for 3-dimensional systems [36,42]. We will report on results from such studies in a subsequent work.…”

Section: Discussionmentioning

confidence: 99%

Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

et al. 2019

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Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with scaling exponents α = 3β and β = −1/5. We argue that these values can be obtained from parametric estimates within kinetic theory indicating the dominance of small momentum transfer in the scattering processes. We also extract the Debye mass non-perturbatively from a longitudinally polarized correlator and observe an IR enhancement of the scalar correlation function for low momenta below the Debye mass.2 We expect the results to carry over to SU(3) theories as well.The qualitative agreement of weakly-coupled SU(Nc) theories far from equilibrium for Nc = 2, 3 has been observed for different phenomena [31][32][33].arXiv:1907.05892v1 [hep-ph]

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Section: Discussionmentioning

confidence: 99%

Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

et al. 2019

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“…Since our results are based on a large-N expansion, it would be very interesting to also analyze the behavior of weakly-coupled systems with small N using real-time lattice simulations along the lines of Refs. [26,27].…”

Section: Discussionmentioning

confidence: 99%

“…9. We can determine the parameters γ p , ω p and F 0 by fitting our data to either (26) or (27). Since the Fourier Wigner space propagators are numerically obtained by a discrete Fourier transformation of the Wigner propagators, both methods are equivalent up to numerical uncertainties.…”

Section: A Violations Of the Fluctuation-dissipation Relationmentioning

confidence: 99%

“…While in thermal equilibrium the spectral (commutator) and statistical (anti-commutator) correlation functions are related by the fluctuation-dissipation relation, this is violated out of equilibrium in general. The question of whether some generalized fluctuationdissipation relation may be defined, such as underlying effective kinetic descriptions of the dynamics, has been recently addressed in this context with the help of classical-statistical simulations [26,27]. Here we compute both spectral and statistical correlation functions directly based on the underlying quantum field.…”

Section: Introductionmentioning

confidence: 99%

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Spectral, statistical, and vertex functions in scalar quantum field theory far from equilibrium

Shen

Berges

2020

Phys. Rev. D

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We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 spacetime dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators and the four-vertex in a self-similar regime in time and space or momenta. The scaling form of the momentum-dependent four-vertex exhibits a dramatic fall-off towards low momenta. Comparing spectral functions (commutators) and statistical correlations (anti-commutators) of field operators allows us to detect strong violations of the fluctuation-dissipation relation in this non-perturbative infrared regime. Based on a self-consistent expansion in the number of field components to next-to-leading order, a wide range of interaction strengths is analyzed and compared to weak-coupling estimates in effective kinetic theory and classical-statistical field theory.

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“…(6) (see e.g. [36]), it turns out that handling the Poisson bracket is impractical and there is a more elegant way to calculate equilibrium spectral functions in classical-statistical field theory [22]. Exploiting the fluctuation dissipation relation for ω T in the classical-statistical theory, Eq.…”

Section: Spectral Functions Fluctuation-dissipation Theorem and Clasmentioning

confidence: 99%

Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations

2020

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We calculate spectral functions of the relativistic O(4) model from real-time lattice simulations in classical-statistical field theory. While in the low and high temperature phase of the model, the spectral functions of longitudinal (σ) and transverse (π) modes are well described by relativistic quasi-particle peaks, we find a highly non-trivial behavior of the spectral functions in the cross over region, where additional structures appear. Similarly, we observe a significant broadening of the quasi-particle peaks, when the amount explicit O(4) symmetry breaking is reduced. We further demonstrate that in the vicinity of the O(4) critical point, the spectral functions develop an infrared power law associated with the critical dynamics, and comment on the extraction of the dynamical critical exponent z from our simulations. ω J = 0.05 / 2 9 J = 0.05 / 2 8 J = 0.05 / 2 7 J = 0.05 / 2 6 J = 0.05 / 2 5 J = 0.05 / 2 4 J = 0.05 / 2 3 J = 0.05 / 2 2 J = 0.05 / 2 J = 0.05 0 50 100 150 200 250 300 350 400 450 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 ρ σ ω J = 0.05 / 2 9 J = 0.05 / 2 8 J = 0.05 / 2 7 J = 0.05 / 2 6 J = 0.05 / 2 5 J = 0.05 / 2 4 J = 0.05 / 2 3 J = 0.05 / 2 2 J = 0.05 / 2 J = 0.05

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Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes

Cited by 22 publications

References 25 publications

Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

Highly occupied gauge theories in 2+1 dimensions: A self-similar attractor

Spectral, statistical, and vertex functions in scalar quantum field theory far from equilibrium

Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations

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