Boltzmann equation solver adapted to emergent chemical nonequilibrium
Abstract
We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical nonequilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical nonequilibrium by studying a model problem that is motivated by the physics of the neutrino freezeout processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup ±}annihilation)
 Authors:
 Program in Applied Mathematics, The University of Arizona, Tucson, AZ, 85721 (United States)
 (United States)
 Department of Mathematics and Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94721 (United States)
 Department of Physics, The University of Arizona, Tucson, AZ, 85721 (United States)
 Publication Date:
 OSTI Identifier:
 22382173
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANNIHILATION; BOLTZMANN EQUATION; CAPTURE; ELECTRONPOSITRON INTERACTIONS; ENERGY DENSITY; EQUILIBRIUM; FREEZING OUT; NEUTRINOS; PHASE SPACE; POLYNOMIALS; RELATIVISTIC RANGE; TIME DEPENDENCE; UNIVERSE
Citation Formats
Birrell, Jeremiah, Email: jeremey.birrell@gmail.com, Department of Physics, The University of Arizona, Tucson, AZ, 85721, Wilkening, Jon, and Rafelski, Johann. Boltzmann equation solver adapted to emergent chemical nonequilibrium. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.10.056.
Birrell, Jeremiah, Email: jeremey.birrell@gmail.com, Department of Physics, The University of Arizona, Tucson, AZ, 85721, Wilkening, Jon, & Rafelski, Johann. Boltzmann equation solver adapted to emergent chemical nonequilibrium. United States. doi:10.1016/J.JCP.2014.10.056.
Birrell, Jeremiah, Email: jeremey.birrell@gmail.com, Department of Physics, The University of Arizona, Tucson, AZ, 85721, Wilkening, Jon, and Rafelski, Johann. 2015.
"Boltzmann equation solver adapted to emergent chemical nonequilibrium". United States.
doi:10.1016/J.JCP.2014.10.056.
@article{osti_22382173,
title = {Boltzmann equation solver adapted to emergent chemical nonequilibrium},
author = {Birrell, Jeremiah, Email: jeremey.birrell@gmail.com and Department of Physics, The University of Arizona, Tucson, AZ, 85721 and Wilkening, Jon and Rafelski, Johann},
abstractNote = {We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical nonequilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ(t) such that the zeroth order term of the basis alone captures the particle number density and energy density of each particle distribution. We validate our method and illustrate the reduced computational cost and the ability to easily represent final state chemical nonequilibrium by studying a model problem that is motivated by the physics of the neutrino freezeout processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e{sup ±}annihilation)},
doi = {10.1016/J.JCP.2014.10.056},
journal = {Journal of Computational Physics},
number = ,
volume = 281,
place = {United States},
year = 2015,
month = 1
}

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