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Register a new userDynamics of Relativistic Interacting Gases : from a Kinetic to a Fluid Description
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Added by
Jean-Philippe Uzan du Darc
Publication date
1998
fields
Physics
and research's language is
English
Authors
Jean-Philippe Uzan
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Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this equation to obtain an effective macroscopic description. This formalism will be useful to study the cosmic microwave background non-perturbatively in inhomogeneous cosmologies. It should also be useful for the study of the dynamics of the early universe and can be applied, if one considers fluids of galaxies, to the study of structure formation.
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We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latters definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.
We present the results of deriving the Israel-Stewart equations of relativistic dissipative fluid dynamics from kinetic theory via Grads 14-moment expansion. Working consistently to second order in the Knudsen number, these equations contain several new terms which are absent in previous treatments.
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolmantextquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by textquotedblleft suppressingtextquotedblright{} the molecular acceleration in Boltzmanntextquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
After a sudden disruption, weakly interacting quantum systems first relax to a prethermalized state that can be described by perturbation theory and a generalized Gibbs ensemble. Using these properties of the prethermalized state we perturbatively derive a kinetic equation which becomes a quantum Boltzmann equation in the scaling limit of vanishing interaction. Applying this to interaction quenches in the fermionic Hubbard model we find that the momentum distribution relaxes to the thermal prediction of statistical mechanics. For not too large interaction, this two-stage scenario provides a quantitative understanding of the time evolution leading from the initial pure via a metastable prethermal to the final thermal state.
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio $eta/s$. We also find that a good agreement between these two approaches requires a Knudsen number $Kn < 1/2$.
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