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Title: Properties of the Boltzmann equation in the classical approximation

Abstract

We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.

Authors:
 [1];  [1];  [2];  [1]
  1. Institut de Physique Theorique, Gif-sur-Yvette Cedex (France)
  2. RIKEN, Wako (Japan); Brookhaven National Lab., Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1188218
Report Number(s):
BNL-107804-2015-JA
Journal ID: ISSN 1550-7998; PRVDAQ; KB0301020
Grant/Contract Number:  
SC00112704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. D, Particles, Fields, Gravitation and Cosmology
Additional Journal Information:
Journal Volume: 90; Journal Issue: 12; Journal ID: ISSN 1550-7998
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Epelbaum, Thomas, Gelis, François, Tanji, Naoto, and Wu, Bin. Properties of the Boltzmann equation in the classical approximation. United States: N. p., 2014. Web. doi:10.1103/PhysRevD.90.125032.
Epelbaum, Thomas, Gelis, François, Tanji, Naoto, & Wu, Bin. Properties of the Boltzmann equation in the classical approximation. United States. https://doi.org/10.1103/PhysRevD.90.125032
Epelbaum, Thomas, Gelis, François, Tanji, Naoto, and Wu, Bin. 2014. "Properties of the Boltzmann equation in the classical approximation". United States. https://doi.org/10.1103/PhysRevD.90.125032. https://www.osti.gov/servlets/purl/1188218.
@article{osti_1188218,
title = {Properties of the Boltzmann equation in the classical approximation},
author = {Epelbaum, Thomas and Gelis, François and Tanji, Naoto and Wu, Bin},
abstractNote = {We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since one has also access to the non-approximated result for comparison.},
doi = {10.1103/PhysRevD.90.125032},
url = {https://www.osti.gov/biblio/1188218}, journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
issn = {1550-7998},
number = 12,
volume = 90,
place = {United States},
year = {Tue Dec 30 00:00:00 EST 2014},
month = {Tue Dec 30 00:00:00 EST 2014}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 19 works
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Works referenced in this record:

Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
journal, April 2014


Color Glass Condensate in Schwinger–Keldysh QCD
journal, January 2014


Gluon transport equation in the small angle approximation and the onset of Bose–Einstein condensation
journal, December 2013


Boltzmann equation in classical and quantum field theory
journal, July 2005


Some features of the glasma
journal, June 2006


UV cascade in classical Yang-Mills theory via kinetic theory
journal, April 2014


Transformations of real-time finite-temperature Feynman rules
journal, September 1994


The Color Glass Condensate
journal, November 2010


Particle production in field theories coupled to strong external sources, I: Formalism and main results
journal, October 2006


Role of quantum fluctuations in a system with strong fields: Spectral properties and thermalization
journal, December 2011


Theory of Many-Particle Systems. I
journal, September 1959


The evolving Glasma
journal, January 2012


Pressure Isotropization in High Energy Heavy Ion Collisions
journal, December 2013


Approach to Equilibrium in Weakly Coupled Non-Abelian Plasmas
journal, October 2014


Kinetics of Bose Condensation
journal, April 1995


The initial spectrum of fluctuations in the little bang
journal, December 2011


Universal attractor in a highly occupied non-Abelian plasma
journal, June 2014


Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow
journal, January 2011


Nonrenormalizability of the classical statistical approximation
journal, September 2014


High energy factorization in nucleus-nucleus collisions. I
journal, September 2008


Dynamical formation of a Bose–Einstein condensate
journal, May 2001


Nonlinear amplification of instabilities with longitudinal expansion
journal, April 2012


Brownian Motion of a Quantum Oscillator
journal, May 1961


Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations
journal, May 2014


Overpopulated gauge fields on the lattice
journal, October 2012


The unstable glasma
journal, August 2006


The Boltzmann equation in classical Yang–Mills theory
journal, May 2014


Fluctuations of the initial color fields in high-energy heavy-ion collisions
journal, October 2013


Loops and trees
journal, May 2011


Initial singularity of the little bang
journal, April 2007


Condensation of bosons in the kinetic regime
journal, January 1997