Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics - INSPIRE

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Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics

Xu-Guang Huang
(
- Frankfurt U., FIAS and
- Frankfurt U.
)
,
Takeshi Kodama
(
- Rio de Janeiro Federal U.
)
,
Tomoi Koide
(
- Frankfurt U., FIAS
)
,
Dirk H. Rischke
(
- Frankfurt U., FIAS and
- Frankfurt U.
)

Oct, 2010

23 pages

Published in:

Phys.Rev.C 83 (2011) 024906

e-Print:

1010.4359 [nucl-th]

DOI:

10.1103/PhysRevC.83.024906

View in:

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Abstract: (arXiv)

The microscopic formulae of the bulk viscosity

\zeta

and the corresponding relaxation time

\tau_{\Pi}

in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae 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

\tau_{\Pi}

and

\zeta

are related as

\tau_{\Pi}=\zeta /[\beta \{(1/3-c_{s}^{2})(\epsilon +P)-2(\epsilon -3P)/9\}]

, where

\epsilon

,

P

and

c_{s}

are the energy density, pressure and velocity of sound, respectively. The predicted

\zeta

and

% \tau_{\Pi}

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 the three approaches are consistent with the causality condition.

24.10.Jv
25.75.-q
47.75.+f
24.10.Nz
fluid: relativistic
quantum chromodynamics: critical phenomena
perturbation theory: chiral
tensor: energy-momentum
higher-order: 0
causality

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