Far-from-equilibrium dynamics with broken symmetries from the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math>expansion of the 2PI effective action

Aarts, Gert; Ahrensmeier, Daria; Baier, Rudolf; Berges, Jürgen; Serreau, Julien

doi:10.1103/physrevd.66.045008

Cited by 208 publications

(326 citation statements)

References 46 publications

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“…To obtain a practically solvable set of dynamic equations, we derive the flow equation for the proper n-point Green function Γ (n) τ by taking the nth field derivative of Eq. (6). Fig.…”

Section: Fig 2: (Color Online)mentioning

confidence: 99%

“…4. Second, Γ (6) τ is one-particle irreducible. Its contribution to the flow of Γ (4) τ does not give rise to bubblechains, even if inserted recursively into the first diagram on the right-hand side of the flow equation for Γ (4) τ .…”

Section: Fig 2: (Color Online)mentioning

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%

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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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“…To obtain a practically solvable set of dynamic equations, we derive the flow equation for the proper n-point Green function Γ (n) τ by taking the nth field derivative of Eq. (6). Fig.…”

Section: Fig 2: (Color Online)mentioning

confidence: 99%

Section: Fig 2: (Color Online)mentioning

confidence: 99%

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confidence: 99%

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

2008

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“…The BVA truncation scheme of the Schwinger-Dyson equations is most easily obtained from the 2PI effective action [17,18,19]. Other approaches leading to these equations are found in [1,15]. Using the extended fields notation, φ α (x) = [χ(x), φ 1 (x), φ 2 (x), .…”

Section: The Classical Action and Time Evolution In The Bvamentioning

confidence: 99%

“…al. [11,12,13,14,15], have looked at a related approximation based on the two-particle irreducible expansion (which they call 2PI-1/N). These investigators have pointed out that when there is broken symmetry, the BVA contains terms not included in the 1/N resummation at next to leading order.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

2003

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We perform a detailed numerical investigation of the dynamics of a single component broken symmetry λ φ 4 field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of φ(0) , and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: Hartree, BVA and a related 2PI-1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how φ(t) and χ(t) depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for φ(t) .

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Introduction

Millington

2013

Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics

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Far-from-equilibrium dynamics with broken symmetries from the1/Nexpansion of the 2PI effective action

Cited by 208 publications

References 46 publications

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

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

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

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