Tuesday, June 12, 2012

1206.1929 (Kyosuke Tsumura et al.)

Derivation of relativistic hydrodynamic equations consistent with
relativistic Boltzmann equation by renoramalization-group method
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Kyosuke Tsumura, Teiji Kunihiro
We apply the renormalization-group method to obtain the first-order relativistic hydrodynamics of the relativistic Boltzmann equation (RBE) as a dynamical system: We explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame. It is argued that the frame on which the flow of relativistic hydrodynamic equation is defined must be the energy frame, i.e., the Landau-Lifshitz one, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order hydrodynamic equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory give the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.
View original: http://arxiv.org/abs/1206.1929

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