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Title: Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics

Abstract

The microscopic formulas of the bulk viscosity {zeta} and the corresponding relaxation time {tau}{sub {Pi}} 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 {tau}{sub {Pi}} and {zeta} are related as {tau}{sub {Pi}={zeta}}/[{beta}{l_brace}(1/3-c{sub s}{sup 2})({epsilon}+P)-2({epsilon}-3P)/9{r_brace}], where {epsilon}, P, and c{sub s} are the energy density, pressure, and velocity of sound, respectively. The predicted {zeta} and {tau}{sub {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 three approaches are consistent with the causality condition.

Authors:
;  [1];  [2];  [1]
  1. Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main (Germany)
  2. Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postale 68528, 21945-970, Rio de Janeiro (Brazil)
Publication Date:
OSTI Identifier:
21499432
Resource Type:
Journal Article
Journal Name:
Physical Review. C, Nuclear Physics
Additional Journal Information:
Journal Volume: 83; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevC.83.024906; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2813
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; APPROXIMATIONS; CAUSALITY; CHIRALITY; COMPARATIVE EVALUATIONS; ENERGY DENSITY; ENERGY-MOMENTUM TENSOR; FLUID MECHANICS; FLUIDS; PERTURBATION THEORY; PHASE TRANSFORMATIONS; PROJECTION OPERATORS; QUANTUM CHROMODYNAMICS; RELATIVISTIC RANGE; RELAXATION TIME; SOUND WAVES; STRING MODELS; STRING THEORY; VELOCITY; VISCOSITY; CALCULATION METHODS; COMPOSITE MODELS; ENERGY RANGE; EVALUATION; EXTENDED PARTICLE MODEL; FIELD THEORIES; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; M-THEORY; PARTICLE MODELS; PARTICLE PROPERTIES; QUANTUM FIELD THEORY; QUARK MODEL; TENSORS

Citation Formats

Xuguang, Huang, Rischke, Dirk H, Institut fuer Theoretische Physik, J.W. Goethe-Universitaet, D-60438 Frankfurt am Main, Kodama, Takeshi, and Koide, Tomoi. Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics. United States: N. p., 2011. Web. doi:10.1103/PHYSREVC.83.024906.
Xuguang, Huang, Rischke, Dirk H, Institut fuer Theoretische Physik, J.W. Goethe-Universitaet, D-60438 Frankfurt am Main, Kodama, Takeshi, & Koide, Tomoi. Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics. United States. https://doi.org/10.1103/PHYSREVC.83.024906
Xuguang, Huang, Rischke, Dirk H, Institut fuer Theoretische Physik, J.W. Goethe-Universitaet, D-60438 Frankfurt am Main, Kodama, Takeshi, and Koide, Tomoi. 2011. "Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics". United States. https://doi.org/10.1103/PHYSREVC.83.024906.
@article{osti_21499432,
title = {Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics},
author = {Xuguang, Huang and Rischke, Dirk H and Institut fuer Theoretische Physik, J.W. Goethe-Universitaet, D-60438 Frankfurt am Main and Kodama, Takeshi and Koide, Tomoi},
abstractNote = {The microscopic formulas of the bulk viscosity {zeta} and the corresponding relaxation time {tau}{sub {Pi}} 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 {tau}{sub {Pi}} and {zeta} are related as {tau}{sub {Pi}={zeta}}/[{beta}{l_brace}(1/3-c{sub s}{sup 2})({epsilon}+P)-2({epsilon}-3P)/9{r_brace}], where {epsilon}, P, and c{sub s} are the energy density, pressure, and velocity of sound, respectively. The predicted {zeta} and {tau}{sub {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 three approaches are consistent with the causality condition.},
doi = {10.1103/PHYSREVC.83.024906},
url = {https://www.osti.gov/biblio/21499432}, journal = {Physical Review. C, Nuclear Physics},
issn = {0556-2813},
number = 2,
volume = 83,
place = {United States},
year = {Tue Feb 15 00:00:00 EST 2011},
month = {Tue Feb 15 00:00:00 EST 2011}
}