Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics

2010/10/21 by Xu-Guang Huang, T. Kodama, Takeshi Kodama +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Causality (physics) #Classical mechanics #Cosmology and Gravitation Theories #Dissipative system #High-Energy Particle Collisions Research #Kinetic energy #Mathematical physics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum electrodynamics #Quantum mechanics #Relaxation (psychology) #Viscosity #Volume viscosity #cond-mat.stat-mech #hep-ph #nucl-th #physics.flu-dyn

paper · pdf · doi:10.1103/physrevc.83.024906

published as Phys.Rev.C83:024906,2011 · 23 pages, 2 figures

arxiv created 2010/10/21 · openalex publication_date 2011/02/14 · arxiv updated 2011/02/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The microscopic formulas of the bulk viscosity \ensuremathζ and the corresponding relaxation time \ensuremathτ_\ensuremathΠ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulas to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading-order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition, and \ensuremathτ_\ensuremathΠ and \ensuremathζ are related as \ensuremathτ_\ensuremathΠ=\ensuremathζ/[\ensuremathβ(1/3\ensuremath-c_s²)(\ensuremathε+P)\ensuremath-2(\ensuremathε\ensuremath-3P)/9], where \ensuremathε, P, and c_s are the energy density, pressure, and velocity of sound, respectively. The predicted \ensuremathζ and \ensuremathτ_\ensuremathΠ should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all three approaches are consistent with the causality condition.

Citations

• From reversible quantum microdynamics to irreversible quantum transport
• Microscopic formula for transport coefficients of causal hydrodynamics
• Enhancement of critical slowing down in chiral phase transition—Langevin dynamics approach
• Formulating viscous hydrodynamics for large velocity gradients
• Anisotropic hydrodynamics, bulk viscosities, andr-modes of strange quark stars with strong magnetic fields
• Why hyperbolic theories of dissipation cannot be ignored: Comment on a paper by Kostädt and Liu
• A New Expansion of the Heisenberg Equation of Motion with Projection Operator
• Derivation of Transport Equations Using the Time-Dependent Projection Operator Method
• Extensivity of irreversible current and stability in causal dissipative hydrodynamics
• Universal properties of bulk viscosity near the QCD phase transition
• Relativistic dissipative hydrodynamics: A minimal causal theory
• Divergence-type nonlinear conformal hydrodynamics
• Transport, Collective Motion, and Brownian Motion
• A new improved energy-momentum tensor
• Meteorite from the Moon: Petrology of Terrae Clasts and One Mare Clast in ALHA 81005,9