Nonthermal fixed points and the functional renormalization group

Berges, Jürgen; Hoffmeister, G.

doi:10.1016/j.nuclphysb.2008.12.017

Cited by 126 publications

(244 citation statements)

References 39 publications

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“…However, the system features a dynamical instability which manifests itself in the growth of modes close to k * . At early times the momentum range of the instability is in excellent agreement with our analytical estimate as can been seen from the squared dispersion relation (14) displayed in the inset. At some intermediate time, additional modes around 3k * become occupied.…”

Section: Secondariessupporting

confidence: 88%

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Inflationary preheating dynamics with two-species condensates

2017

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We discuss the amplification of loop corrections in quantum many-body systems through dynamical instabilities. As an example, we investigate both analytically and numerically a two-component ultracold atom system in one spatial dimension. The model features a tachyonic instability, which incorporates characteristic aspects of the mechanisms for particle production in early-universe inflaton models. We establish a direct correspondence between measureable macroscopic growth rates for occupation numbers of the ultracold Bose gas and the underlying microscopic processes in terms of Feynman loop diagrams. We analyze several existing ultracold atom setups featuring dynamical instabilities and propose optimized protocols for their experimental realization. We demonstrate that relevant dynamical processes can be enhanced using a seeding procedure for unstable modes and clarify the role of initial quantum fluctuations and the generation of a non-linear secondary stage for the amplification of modes.

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Section: Secondariessupporting

confidence: 88%

“…where H = H 0 + 2g 12 µ2 g2 − µ 1 and similiar for F 21 , F 22 from which we recover the Bogoliubov result (14). As long asφ 1 = 0, the 1, 2 components decouple from the 3, 4 components of F and e.g.…”

Section: Proposal Of Seeding Proceduressupporting

confidence: 81%

Inflationary preheating dynamics with two-species condensates

2017

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“…We consider n 0 = 39 as well as n 0 = 7.5. 3 The characteristic scale Q given by (2.12) is taken to be always the same, thus fixing Q 0 for given n 0 . We employ a weak coupling λ = 10 −4 .…”

Section: Basin Of Attraction For the Nonthermal Fixed Pointmentioning

confidence: 99%

“…The self-similar time-evolution within a given universality class of different models can then be mapped onto each other by simple rescalings. The universal properties are described in terms of nonthermal fixed points [2] in renormalization group theory [3]. While the notion of thermal fixed points describing different universality classes is well established for systems in thermal equilibrium, the corresponding classification for nonequilibrium scaling phenomena is a rapidly progressing research topic.…”

Section: Introductionmentioning

confidence: 99%

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Berges

Boguslavski

Schlichting

et al. 2014

J. High Energ. Phys.

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Different thermalization scenarios for systems with large fields have been proposed in the literature based on classical-statistical lattice simulations approximating the underlying quantum dynamics. We investigate the range of validity of these simulations for condensate driven as well as fluctuation dominated initial conditions for the example of a single component scalar field theory. We show that they lead to the same phenomenon of turbulent thermalization for the whole range of (weak) couplings where the classicalstatistical approach is valid. In the turbulent regime we establish the existence of a dual cascade characterized by universal scaling exponents and scaling functions. This complements previous investigations where only the direct energy cascade has been studied for the single component theory. A proposed alternative thermalization scenario for stronger couplings is shown to be beyond the range of validity of classical-statistical simulations.

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“…[23,24] and [25]. The goal of [25] was the investigation of non-thermal fixed points. Many technical problems -for example specifying a proper regulator function in Minkowski space -could be avoided in [25] by integrating the flow equation and using a 1/N expansion to determine scaling relations between different correlation functions at a non-equilibrium fixed point.…”

Section: Jhep05(2012)021mentioning

confidence: 99%

Analytic continuation of functional renormalization group equations

Floerchinger

2012

J. High Energ. Phys.

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Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N ) symmetry we discuss the analytic structure of the flowing action and show how it is possible to derive and solve flow equations for real-time properties such as propagator residues and particle decay widths. The formalism conserves space-time symmetries such as Lorentz or Galilei invariance and allows for improved, self-consistent approximations in terms of derivative expansions in Minkowski space.

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Nonthermal fixed points and the functional renormalization group

Cited by 126 publications

References 39 publications

Inflationary preheating dynamics with two-species condensates

Inflationary preheating dynamics with two-species condensates

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Analytic continuation of functional renormalization group equations

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