Quantum dynamics of phase transitions in broken symmetry<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>field theory

Cooper, Fred; Dawson, John F.; Mihaila, Bogdan

doi:10.1103/physrevd.67.056003

Cited by 64 publications

(23 citation statements)

References 36 publications

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“…The situation is reminiscent of some aspects of the anisotropic initial stage in the central region of two colliding wave packets. 5 Of course, a peaked initial particle number distribution is not very specific and is thought to exhibit characteristic properties of nonequilibrium dynamics for a large variety of physical situations.…”

Section: Comparison Of Lo Nlo and "Full" Resultsmentioning

confidence: 99%

“…There has been important progress in our understanding of nonequilibrium quantum fields using suitable resummation techniques based on 2PI generating functionals [2]. They have been successfully used to describe far-fromequilibrium dynamics and subsequent thermalization in quantum field theory [3,4,5,6,7,8]. While it is difficult to test analytic approximations for theories such as QCD, where strong interactions play an important role, the description of scalar and fermionic theories for not too strong couplings seems well under quantitative control by now.…”

Section: Introductionmentioning

confidence: 99%

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Range of validity of transport equations

Berges

Borsányi

2006

Phys. Rev. D

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Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss is in general not controlled by a small expansion parameter. We determine the range of validity of transport equations for the example of a scalar g 2 Φ 4 theory. We solve the nonequilibrium time evolution using the threeloop 2PI effective action. The approximation includes off-shell and memory effects and assumes no gradient expansion. This is compared to transport equations to lowest order (LO) and beyond (NLO). We find that the earliest time for the validity of transport equations is set by the characteristic relaxation time scale t damp = −2ω/Σ (eq) ̺ , where −Σ (eq) ̺ /2 denotes the on-shell imaginary-part of the self-energy. This time scale agrees with the characteristic time for partial memory loss, but is much shorter than thermal equilibration times. For times larger than about t damp the gradient expansion to NLO is found to describe the "full" results rather well for g 2 1. *

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Section: Comparison Of Lo Nlo and "Full" Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Range of validity of transport equations

Berges

Borsányi

2006

Phys. Rev. D

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“…Some more genuine nonperturbative effects can be captured by combining the 2PI effective action with a large-N type expansion [12,13]. In the nonequilibrium context the 2PI 1/N expansion at next-toleading order proved to be particularly fruitful for the study of a variety of problems, such that thermalization [12][13][14], preheating [15,16], transport coefficients [17][18][19], nonthermal fixed points [20], decoherence [21], and topological defect formation [22,23]. In equilibrium, the 2PI formalism was applied to phenomenological studies in various approximations, see [24] and references therein as well as [25,26].…”

Section: Introductionmentioning

confidence: 99%

Broken phase scalar effective potential andΦ-derivable approximations

Reinosa

Szép

2011

Phys. Rev. D

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We study the effective potential of a real scalar ' 4 theory as a function of the temperature T within the simplest È-derivable approximation, namely, the Hartree approximation. We apply renormalization at a ''high'' temperature T ? where the theory is required to be in its symmetric phase and study how the effective potential evolves as the temperature is lowered down to T ¼ 0. In particular, we prove analytically that no second order phase transition can occur in this particular approximation of the theory, in agreement with earlier studies based on the numerical evaluation or the high temperature expansion of the effective potential. This work is also an opportunity to illustrate certain issues on the renormalization of È-derivable approximations at finite temperature and nonvanishing field expectation value and to introduce new computational techniques which might also prove useful when dealing with higher order approximations.

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“…Note that all terms with first order gradients have disappeared in (60) and (61). A first consequence of (61) is a direct relation between the real and the imaginary parts of the retarded/advanced Green function, which reads (forΓ = 0):…”

Section: Derivation Of Off-shell Transport Theorymentioning

confidence: 99%

“…The numerical solutions are also obtained only for homogenous systems, so far (cf. [58][59][60][61][62][63]). …”

Section: Introductionmentioning

confidence: 99%

From Kadanoff-Baym dynamics to off-shell parton transport

Cassing

2009

Eur. Phys. J. Spec. Top.

175

354

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Abstract. The description of strongly interacting quantum fields is based on twoparticle irreducible (2PI) approaches that allow for a consistent treatment of quantum systems out-of-equilibrium as well as in thermal equilibrium. As a theoretical test case the quantum time evolution of Φ 4 -field theory in 2+1 space-time dimensions is investigated numerically for out-of-equilibrium initial conditions on the basis of the Kadanoff-Baym-equations including the tadpole and sunset self energies. In particular we address the dynamics of the spectral ('off-shell') distributions of the excited quantum modes and the different phases in the approach to equilibrium described by Kubo-Martin-Schwinger relations for thermal equilibrium states. A detailed comparison of the full quantum dynamics to approximate schemes like that of a standard kinetic (on-shell) Boltzmann equation is performed. We find that far off-shell 1 ↔ 3 processes are responsible for chemical equilibration, which is not included in the Boltzmann limit. Furthermore, we derive generalized transport equations for the same theory in a first order gradient expansion in phase space thus explicitly retaining the off-shell dynamics as inherent in the time-dependent spectral functions. The solutions of these equations compare very well with the exact solutions of the full Kadanoff-Baym equations with respect to the occupation numbers of the individual modes, the spectral evolution as well as the chemical equilibration process. Furthermore, the proper equilibrium off-shell distribution is reached for large times contrary to the quasiparticle Boltzmann limit. We additionally present a direct comparison of the solution of the generalized transport equations in the Kadanoff-Baym (KB) and Botermans-Malfliet (BM) form; both solutions are found to agree very well with each other. The off-shell transport equation in the BM scheme allows for an explicit solution within an extended dynamical quasiparticle Ansatz. This leads to generalized equations of motion for dynamical quasiparticles that exceed the classical Hamilton equations and allow for the description of dynamical spectral functions. The dynamical quasiparticle model (DQPM) is used to extract partonic spectral functions from lattice QCD in the temperature range 0.8 ≤ T /Tc ≤ 10. By consideration of time-like and space-like sectors of 'observables' such as number densities, energy densities etc. mean-field potentials as well as effective interactions are extracted at different temperature T and quark chemical potentials µq. The latter determine the off-shell dynamics in the Parton-Hadron-String Dynamics (PHSD) transport approach. Illustrative examples for off-shell dynamics in the hadron and parton sector are presented for e + e − production from nucleusnucleus collisions from SIS to RHIC energies. The generalized transport approach, furthermore, qualifies for the description of hadronization without leading to the problem of entropy reduction as in conventional coalescence models.

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Quantum dynamics of phase transitions in broken symmetryλφ4field theory

Cited by 64 publications

References 36 publications

Range of validity of transport equations

Range of validity of transport equations

Broken phase scalar effective potential andΦ-derivable approximations

From Kadanoff-Baym dynamics to off-shell parton transport

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