Prethermalization

Berges, Jürgen; Borsányi, Szabolcs; Wetterich, C.

doi:10.1103/physrevlett.93.142002

Cited by 527 publications

(779 citation statements)

References 17 publications

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“…As a consequence, a wide range of growing modes lead to a prethermalization of the equation of state at the end of this early stage [1,49,50] while the distribution function itself is still far from equilibrium.…”

Section: Jhep05(2014)054mentioning

confidence: 99%

“…Therefore any thermalization process starting from a nonequilibrium initial state requires an effective loss of details about the initial conditions at sufficiently long times. It was pointed out previously that an effective partial memory loss of initial condition details can already be observed at earlier stages for the nonequilibrium unitary time evolution in quantum field theory [1].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Jhep05(2014)054mentioning

confidence: 99%

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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“…Hence, the precise way in which the cutoff R τ,ab diverges at t a = t b > τ is chosen such that Γ (2) τ +R τ is the inverse of −iG τ for all times t a , t b , see Eq. (8). Using Eq.…”

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confidence: 99%

“…[2], as well as techniques for exactly solvable models [3]. Non-perturbative approximations of the two-particle irreducible (2PI) effective action [4] have been intensively studied and applied to nonequilibrium dynamics [5,6,7,8,9,10,11] and are applicable also in more than one dimension. In field theory, they also provide a way to study strongly correlated fermions beyond mean-field and Boltzmann approximations [8].…”

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confidence: 99%

Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach

2008

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Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time evolution of the Green functions is computed within a vertex expansion. It is shown that this agrees with the dynamics derived from the 1/N -expansion of the two-particle irreducible effective action.PACS numbers: 03.75. Kk, 05.10.Cc, 05.70.Ln, Introduction. Far-from-equilibrium quantum field dynamics is one of the most challenging issues both in experimental and theoretical physics to date. Experiments exhibiting quantum statistical effects in the time evolution of many-body systems are extremely demanding. In particular, the preparation of ultracold atomic Bose and Fermi gases in various trapping environments allows to precisely study quantum many-body dynamics of strongly correlated systems, see, e.g., Refs.[1]. In recent years, the field has attracted researchers from a variety of disciplines, ranging from condensed-matter to highenergy particle physics and cosmology. Nonequilibrium field theory to date is dominated by semi-classical mean-field approaches which are in general only valid for weak interactions or large occupation numbers. For strongly correlated quantum systems methods are available predominantly for systems in one spatial dimension and include the Density Matrix Renormalisation Group methods, see e.g. [2], as well as techniques for exactly solvable models [3]. Non-perturbative approximations of the two-particle irreducible (2PI) effective action [4] have been intensively studied and applied to nonequilibrium dynamics [5,6,7,8,9,10,11] and are applicable also in more than one dimension. In field theory, they also provide a way to study strongly correlated fermions beyond mean-field and Boltzmann approximations [8]. Like these, the results presented here are expected to be of high relevance, e.g., for the description of ultracold degenerate Fermi gases close to the BEC-BCS crossover [12].In this paper we derive dynamic equations for quantum fields far from equilibrium. As a central result, we derive a new time evolution equation for the non-equilibrium effective action by use of functional renormalisation group (RG) techniques, cf. Refs. [13,14,15,16], as well as [17] for non-equilibrium applications. This exact and closed evolution equation allows for non-perturbative approximations that lead substantially beyond mean-field and quantum Boltzmann type approaches: it can be rewritten, in a closed form, as a hierarchy of dynamical equations for Green functions, and this hierarchy admits truncations that neither explicitly nor implicitly rely on small bare couplings or close-to...

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“…In contrast, the 2PI effective action treats soft and hard scales on a different footing thus preventing the presence of unwanted temperature dependent singularities. Finally the use of the 2PI effective action goes now beyond the description of systems in equilibrium since it has been successfully applied to describe late time dynamics of quantum fields out-of-equilibrium [21,22,23,24,25,26,27,28,29,30] and may then be useful in understanding equilibration properties of the system created in ultra-relativistic heavy-ion collisions.…”

Section: Introductionmentioning

confidence: 99%

Non-perturbative renormalization of Φ-derivable approximations in theories with fermions

Reinosa

2006

Nuclear Physics A

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We show how to renormalize Φ-derivable approximations in a theory with a fermionic field coupled to a self-interacting scalar field through a Yukawa interaction. The nonperturbative renormalization concerns the self-interaction coupling of the scalar field which is renormalized via a set of nested Bethe-Salpeter equations for the scalar and fermionic four-point functions. We use this information to construct explicit finite equations of motion in the symmetric phase. We work in the context of equilibrium quantum field theory and show that the renormalization can be carried out without introducing temperature dependent counterterms. * Electronic address: u.reinosa@thphys.uni-heidelberg.de

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Prethermalization

Cited by 527 publications

References 17 publications

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

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

Towards far-from-equilibrium quantum field dynamics: A functional renormalisation-group approach

Non-perturbative renormalization of Φ-derivable approximations in theories with fermions

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