Analytic approach to the relaxation time approximation Boltzmann attractor
Analytic approach to the relaxation time approximation Boltzmann attractor
We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain a series expansion of this system’s far-from-equilibrium attractor. This expansion possesses a finite radius of convergence, which proves the existence of the attractor. Furthermore, the series can be analytically continued to late times and we find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.
Aniceto, Ines
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Noronha, Jorge
cd9c7cbb-cea8-44b6-b21a-0d224d3edf02
Spaliński, Michał
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23 April 2025
Aniceto, Ines
0061ca0c-1ad8-4510-9b12-008e5c27a7ea
Noronha, Jorge
cd9c7cbb-cea8-44b6-b21a-0d224d3edf02
Spaliński, Michał
3fabf22d-7873-492c-8bc6-6101c914c2b0
Aniceto, Ines, Noronha, Jorge and Spaliński, Michał
(2025)
Analytic approach to the relaxation time approximation Boltzmann attractor.
Physical Review D, 111 (7), [076025].
(doi:10.1103/PhysRevD.111.076025).
Abstract
We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain a series expansion of this system’s far-from-equilibrium attractor. This expansion possesses a finite radius of convergence, which proves the existence of the attractor. Furthermore, the series can be analytically continued to late times and we find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.
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2401.06750
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Accepted/In Press date: 21 February 2025
Published date: 23 April 2025
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© 2025 American Physical Society.
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Local EPrints ID: 486797
URI: http://eprints.soton.ac.uk/id/eprint/486797
ISSN: 2470-0037
PURE UUID: ca6ccc48-6cbb-4380-a2ef-054362cc82fe
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Date deposited: 06 Feb 2024 17:40
Last modified: 22 Aug 2025 02:26
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Author:
Jorge Noronha
Author:
Michał Spaliński
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