The non-equilibrium attractor for kinetic theory in relaxation time approximation
Abstract
I demonstrate that the concept of a non-equilibrium attractor can be extended beyond the lowest-order moments typically considered in hydrodynamic treatments. Using a previously obtained exact solution to the relaxation-time approximation Boltzmann equation for a transversally homogeneous and boost-invariant system subject to Bjorken flow, I derive an equation obeyed by all moments of the one-particle distribution function. Using numerical solutions, I show that, similar to the pressure anisotropy, all moments of the distribution function exhibit attractor-like behavior wherein all initial conditions converge to a universal solution after a short time with the exception of moments which are sensitive to modes with zero longitudinal momentum and high transverse momentum. In addition, I compute the exact solution for the distribution function itself on very fine lattices in momentum space and demonstrate that (a) an attractor for the full distribution function exists and (b) solutions with generic initial conditions relax to this solution, first at low momentum and later at high momentum.
- Publication Date:
- Research Org.:
- Kent State Univ., Kent, OH (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1611989
- Grant/Contract Number:
- SC0013470
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 12; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Heavy Ion Phenomenology
Citation Formats
Strickland, M. The non-equilibrium attractor for kinetic theory in relaxation time approximation. United States: N. p., 2018.
Web. doi:10.1007/jhep12(2018)128.
Strickland, M. The non-equilibrium attractor for kinetic theory in relaxation time approximation. United States. https://doi.org/10.1007/jhep12(2018)128
Strickland, M. Fri .
"The non-equilibrium attractor for kinetic theory in relaxation time approximation". United States. https://doi.org/10.1007/jhep12(2018)128. https://www.osti.gov/servlets/purl/1611989.
@article{osti_1611989,
title = {The non-equilibrium attractor for kinetic theory in relaxation time approximation},
author = {Strickland, M.},
abstractNote = {I demonstrate that the concept of a non-equilibrium attractor can be extended beyond the lowest-order moments typically considered in hydrodynamic treatments. Using a previously obtained exact solution to the relaxation-time approximation Boltzmann equation for a transversally homogeneous and boost-invariant system subject to Bjorken flow, I derive an equation obeyed by all moments of the one-particle distribution function. Using numerical solutions, I show that, similar to the pressure anisotropy, all moments of the distribution function exhibit attractor-like behavior wherein all initial conditions converge to a universal solution after a short time with the exception of moments which are sensitive to modes with zero longitudinal momentum and high transverse momentum. In addition, I compute the exact solution for the distribution function itself on very fine lattices in momentum space and demonstrate that (a) an attractor for the full distribution function exists and (b) solutions with generic initial conditions relax to this solution, first at low momentum and later at high momentum.},
doi = {10.1007/jhep12(2018)128},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2018,
place = {United States},
year = {Fri Dec 21 00:00:00 EST 2018},
month = {Fri Dec 21 00:00:00 EST 2018}
}
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Works referencing / citing this record:
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