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Register a new userDynamics and Stability of Chiral Fluid
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Starting from the linear sigma model with constituent quarks we derive the chiral fluid dynamics where hydrodynamic equations for the quark fluid are coupled to the equation of motion for the order-parameter field. In a static system at thermal equilibrium this model leads to a chiral phase transition which, depending on the choice of the quark-meson coupling constant, could be a crossover or a first order one. We investigate the stability of the chiral fluid in the static and expanding backgrounds by considering the evolution of perturbations with respect to the mean-field solution. In the static background the spectrum of plane-wave perturbations consists of two branches, one corresponding to the sound waves and another to the sigma-meson excitations. For large couplings these two branches cross and the excitation spectrum acquires exponentially growing modes. The stability analysis is also done for the Bjorken-like background solution by explicitly solving the time-dependent differential equation for perturbations in the eta-space. In this case the growth rate of unstable modes is significantly reduced.
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We investigate the causality and the stability of the relativistic viscous magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfven and the magneto-sonic modes.In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfven modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.
We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart. We present a frame independent calculation of all first- and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart.
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients carry information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion.
Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function, $hat{f}_{0bf k}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from $hat{f}_{0bf k}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.
The fluid dynamics of a relativistic fireball with longitudinal and transverse expansion is described using a background-fluctuation splitting. Symmetry representations of azimuthal rotations and longitudinal boosts are used for a classification of initial state configurations and their fluid dynamic propagation in terms of a mode expansion. We develop an accurate and efficient numerical scheme based on the pseudo-spectral method to solve the resulting hyperbolic partial differential equations. Comparison to the analytically known Gubser solution underlines the high accuracy of this technique. We also present first applications of FluiduM to central heavy ion collisions at the LHC energies featuring a realistic thermodynamic equations of state as well as shear and bulk viscous dissipation.
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