Properties of the Boltzmann equation in the classical approximation

Epelbaum, Thomas; Gelis, François; Tanji, Naoto; Wu, Bin

doi:10.1103/physrevd.90.125032

Cited by 24 publications

(50 citation statements)

References 41 publications

(89 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More precisely, in this regime, quantum field theory can be mapped onto a classicalstatistical field theory [33,34], which can be simulated numerically. Otherwise, as soon as typical occupation numbers become of order unity, f ≲ 1, the mapping becomes inaccurate [32,[38][39][40], and the system leaves the classical regime, thermalizing eventually [41]. Thus, we restrict ourselves to the case of sufficiently large occupation numbers and study the scalar systems with classicalstatistical simulations in this section.…”

Section: Dynamics For Single-component Model (N = 1)mentioning

confidence: 99%

Attractive versus repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories

et al. 2017

View full text Add to dashboard Cite

We study the impact of attractive self-interactions on the nonequilibrium dynamics of relativistic quantum fields with large occupancies at low momenta. Our primary focus is on Bose-Einstein condensation and nonthermal fixed points in such systems. For a model system, we consider OðNÞ-symmetric scalar field theories. We use classical-statistical real-time simulations as well as a systematic 1=N expansion of the quantum (two-particle-irreducible) effective action to next-to-leading order. When the mean self-interactions are repulsive, condensation occurs as a consequence of a universal inverse particle cascade to the zero-momentum mode with self-similar scaling behavior. For attractive mean selfinteractions, the inverse cascade is absent, and the particle annihilation rate is enhanced compared to the repulsive case, which counteracts the formation of coherent field configurations. For N ≥ 2, the presence of a nonvanishing conserved charge can suppress number-changing processes and lead to the formation of stable localized charge clumps, i.e., Q balls.

show abstract

Section: Dynamics For Single-component Model (N = 1)mentioning

confidence: 99%

Attractive versus repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories

et al. 2017

View full text Add to dashboard Cite

show abstract

“…We also see here a trend already observed in the isotropic case in ref. [32]: the classical approximation leads to more condensation than the unapproximated collision term. In fact, when the ultraviolet cutoff is large compared to the physical momentum scales, most of the particles tend to aggregate in a condensate in the classical approximation.…”

Section: Bose-einstein Condensationmentioning

confidence: 99%

“…It is well known that this Ansatz provides the correct quadratic terms [21,22], accompanied by some spurious terms that are linear in the distribution function. This variant is known to suffer from a severe ultraviolet cutoff dependence, when the cutoff becomes large compared to the physical scales [32] (this property is closely related to the non-renormalizability of a variant of the classical approximation in quantum field theory, where one includes the zero point vacuum fluctuations [33]). For this reason, our algorithm for the Boltzmann equation in a longitudinally expanding system cannot be employed to study this alternate classical approximation, because of its fixed cutoff in p z , while the physical p z s decrease with time due to the expansion.…”

Section: Classical Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Kinetic theory of a longitudinally expanding system of scalar particles

Epelbaum

Gelis

Jeon

et al. 2015

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann equation for a longitudinally expanding system of scalar particles interacting with a φ 4 coupling, that mimics the kinematics of a heavy ion collision at very high energy. We consider only elastic 2 → 2 scatterings, and we allow the formation of a Bose-Einstein condensate in overpopulated situations by solving the coupled equations for the particle distribution and the particle density in the zero mode. For generic CGC-like initial conditions with a large occupation number, the solutions of the full Boltzmann equation cease to display the classical attractor behavior sooner than expected; for moderate coupling, the solutions appear never to follow a classical attractor solution.

show abstract

“…A field theoretic framework that does this is the 2-particle irreducible approximation [10][11][12][13][14][15] of the Kadanoff-Baym equations. A computationally much cheaper alternative is to use kinetic theory [16] in order to investigate the role of quantum fluctuations. The Boltzmann equation with 2 → 2 scatterings reads:…”

Section: Kinetic Theory Approachmentioning

confidence: 99%