### 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 non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ{hooked}(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ{hooked}(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 non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e^{±}-annihilation).

Original language | English (US) |
---|---|

Pages (from-to) | 896-916 |

Number of pages | 21 |

Journal | Journal of Computational Physics |

Volume | 281 |

DOIs | |

State | Published - Jan 5 2015 |

### Fingerprint

### Keywords

- Chemical non-equilibrium
- Orthogonal polynomial spectral method
- Relativistic Boltzmann equation

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Computational Physics*,

*281*, 896-916. https://doi.org/10.1016/j.jcp.2014.10.056

**Boltzmann equation solver adapted to emergent chemical non-equilibrium.** / Birrell, Jeremiah; Wilkening, Jon; Rafelski, Johann.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 281, pp. 896-916. https://doi.org/10.1016/j.jcp.2014.10.056

}

TY - JOUR

T1 - Boltzmann equation solver adapted to emergent chemical non-equilibrium

AU - Birrell, Jeremiah

AU - Wilkening, Jon

AU - Rafelski, Johann

PY - 2015/1/5

Y1 - 2015/1/5

N2 - 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 non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ{hooked}(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ{hooked}(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 non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e±-annihilation).

AB - 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 non-equilibrium. Two time dependent parameters characterize the set of orthogonal polynomials, the effective temperature T(t) and phase space occupation factor ϒ{hooked}(t). In this first paper we address (effectively) massless fermions and derive dynamical equations for T(t) and ϒ{hooked}(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 non-equilibrium by studying a model problem that is motivated by the physics of the neutrino freeze-out processes in the early Universe, where the essential physical characteristics include reheating from another disappearing particle component (e±-annihilation).

KW - Chemical non-equilibrium

KW - Orthogonal polynomial spectral method

KW - Relativistic Boltzmann equation

UR - http://www.scopus.com/inward/record.url?scp=84916893280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84916893280&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2014.10.056

DO - 10.1016/j.jcp.2014.10.056

M3 - Article

AN - SCOPUS:84916893280

VL - 281

SP - 896

EP - 916

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -