Thermalization and Lyapunov exponents in Yang-Mills-Higgs theory

Heinz, Ulrich; Hu, C. R.; Leupold, Stefan; Matinyan, S.G.; Müller, Berndt

doi:10.1103/physrevd.55.2464

Cited by 38 publications

(57 citation statements)

References 17 publications

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“…Whether this is the case for the softer modes needs to be studied further. It would be interesting to relate this approach to that of Müller and collaborators [48,49,50].…”

Section: Discussionmentioning

confidence: 99%

Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

Krasnitz

Venugopalan²

1999

Nuclear Physics B

302

384

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At very high energies, in the infinite momentum frame and in light cone gauge, a hard scale proportional to the high parton density arises in QCD. In an effective theory of QCD at small x, this scale is of order α S µ, where µ is simply related to the gluon density at higher rapidities. The ab initio real time evolution of small x modes in a nuclear collision can be described consistently in the classical effective theory and various features of interest can be studied non-perturbatively. In this paper, we discuss results from a real time SU(2) lattice computation of the production of gluon jets at very high energies. At very large transverse momenta, k t ≥ µ, our results match the predictions from pQCD based mini-jet calculations.Novel non-perturbative behaviour of the small x modes is seen at smaller momenta k t ∼ α S µ.Gauge invariant energy-energy correlators are used to estimate energy distributions evolving in proper time.

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“…Whether this is the case for the softer modes needs to be studied further. It would be interesting to relate this approach to that of Müller and collaborators [48,49,50].…”

Section: Discussionmentioning

confidence: 99%

Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

Krasnitz

Venugopalan²

1999

Nuclear Physics B

302

384

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“…It has been noted in various situations [35,36,37,38,39,40,41,42] that the classical solutions of Yang-Mills equations that constitute the LO answer in the CGC approach are unstable under small perturbations. Practically, this means that loop corrections contain secular divergences -i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, after y 0 ≥ 1000, the mass of the quasi-particles that populate the system decreases slowly with time, indicating that the system is not yet completely equilibrated (the change in the mass of the quasi-particles reflects a change in the occupation number of the various modes of the system, that we will study more directly in the following section). If one takes as a crude estimate the Hard Thermal Loop [56,57] expression of the medium-generated mass (see for instance [58], pp [41][42][43][44][45],…”

Section: Quasi-particle Massmentioning

confidence: 99%

Role of quantum fluctuations in a system with strong fields: Spectral properties and thermalization

Epelbaum

Gelis

2011

Nuclear Physics A

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In a previous work [arXiv:1009.4363], we have studied the evolution of a scalar field with a quartic coupling, driven by a classical source that initializes it to a non-perturbatively large value. At leading order in the coupling, the evolution of this system is given by classical solutions of the field equation of motion. However, this system is subject to a parametric resonance that leads to secular divergences in higher order corrections to physical observables. We have proposed a scheme that resums all the leading secular terms: this resummation leads to finite results at all times, and we have observed also that it makes the pressure tensor of the system relax to its equilibrium value.In the present paper, we continue the study of this system by looking at finer details of its dynamics. We first compute its spectral function at various stages of the evolution, and we observe that after a fairly short transient time there are well defined massive quasi-particles. We then consider the time evolution of the momentum distribution of these quasi-particles, and we show that after a stage dominated by the parametric resonance, this distribution slowly evolves to an equilibrium distribution. Interestingly, this distribution develops a transient chemical potential, signalling the fact that number changing processes are much slower than the elastic ones.

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“…It seems also that we can indirectly associate the chaoticity in the system with the equilibration rates of the fields, in close analogy with the one found between the Lyapunov exponent and the thermalization rate in perturbative thermal gauge theory [17]. We note from the results obtained here and from the numerical simulations we performed, that the smaller is the fractal dimension (or the larger is ǫ) the fastest the fields equilibrate to their asymptotic states by loosing their energies to radiation, which will then eventually thermalize.…”

Section: Discussionmentioning

confidence: 92%

Chaotic symmetry breaking and dissipative two-field dynamics

Ramos

Navarro

2000

Phys. Rev. D

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The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model parameters leading to symmetry breaking along one of the field directions, the symmetry broken vacua make the role of transitory strange attractors and the field trajectories in phase space are strongly chaotic. Chaos is quantified by means of the determination of the fractal dimension, which gives an invariant measure for chaotic behavior. Discussions concerning chaos and dissipation in the model and possible applications to related problems are given.

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Thermalization and Lyapunov exponents in Yang-Mills-Higgs theory

Cited by 38 publications

References 17 publications

Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

Role of quantum fluctuations in a system with strong fields: Spectral properties and thermalization

Chaotic symmetry breaking and dissipative two-field dynamics

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