From moments of the distribution function to hydrodynamics $-$ the non-conformal case - Archive ouverte HAL
Article Dans Une Revue Phys.Rev.C Année : 2022

From moments of the distribution function to hydrodynamics $-$ the non-conformal case

Sunil Jaiswal
  • Fonction : Auteur
Rajeev S. Bhalerao
  • Fonction : Auteur
Zenan Chen
  • Fonction : Auteur
Amaresh Jaiswal
  • Fonction : Auteur
Li Yan
  • Fonction : Auteur

Résumé

We study the one-dimensional boost-invariant Boltzmann equation in the relaxation-time approximation using special moments of the distribution function for a system with a finite particle mass. The infinite hierarchy of moments can be truncated by keeping only the three lowest moments that correspond to the three independent components of the energy-momentum tensor. We show that such a three-moment truncation reproduces accurately the exact solution of the kinetic equation after a simple renormalization that takes into account the effects of the neglected higher moments. We derive second-order Israel-Stewart hydrodynamic equations from the three-moment equations, and show that, for most physically relevant initial conditions, these equations yield results comparable to those of the three-moment truncation, albeit less accurate. We attribute this feature to the fact that the structure of Israel-Stewart equations is similar to that of the three-moment truncation. In particular, the presence of the relaxation term in the Israel-Stewart equations, yields an early-time regime that mimics approximately the collisionless regime. A detailed comparison of the three-moment truncation with second-order non-conformal hydrodynamics reveals ambiguities in the definition of second-order transport coefficients. These ambiguities affect the ability of Israel-Stewart hydrodynamics to reproduce results of kinetic theory.

Dates et versions

hal-03762974 , version 1 (29-08-2022)

Identifiants

Citer

Sunil Jaiswal, Jean-Paul Blaizot, Rajeev S. Bhalerao, Zenan Chen, Amaresh Jaiswal, et al.. From moments of the distribution function to hydrodynamics $-$ the non-conformal case. Phys.Rev.C, 2022, 106 (4), pp.044912. ⟨10.1103/PhysRevC.106.044912⟩. ⟨hal-03762974⟩
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