Anisotropic hydrodynamics for a mixture of quark and gluon fluids

Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radosław; Tinti, Leonardo

doi:10.1103/physrevc.92.054912

Cited by 25 publications

(41 citation statements)

References 45 publications

(81 reference statements)

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“…Tests of this formulation are performed by comparing the results of anisotropic hydorodynamics with the exact solutions of the Boltzmann equations for a mixture of fluids in the Bjorken flow limit. One finds a very good agreement between the hydrodynamic and kinetic-theory results [1]. …”

supporting

confidence: 58%

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Mixture of Quark and Gluon Fluids Described in Terms of Anisotropic Hydrodynamics

Maksymiuk¹

2017

Acta Phys. Pol. B Proc. Suppl.

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A system of equations of anisotropic hydrodynamics that describes mixture of quark and gluon fluids is studied. The equations are based on the zeroth, first, and second moments of the RTA kinetic equations. Tests of this formulation are performed by comparing the results of anisotropic hydorodynamics with the exact solutions of the Boltzmann equations for a mixture of fluids in the Bjorken flow limit. One finds a very good agreement between the hydrodynamic and kinetic-theory results [1].

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supporting

confidence: 58%

“…The equilibrium distribution functions are used to define the RTA collision terms in (1). In this case µ and T should be treated as the effective baryon chemical potential and effective temperature that are determined by the appropriate Landau matching conditions.…”

Section: Kinetic Equationsmentioning

confidence: 99%

Mixture of Quark and Gluon Fluids Described in Terms of Anisotropic Hydrodynamics

Maksymiuk¹

2017

Acta Phys. Pol. B Proc. Suppl.

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“…In Minkowski space with 1 Previous studies of the Bjorken model have shown that after rewriting the hydrodynamical equations for the temperature and the only independent component of the shear viscous tensor in terms of the variable w ¼ τTðτÞ (where τ and T are the longitudinal proper time and temperature) reduce effectively to a truly 1D nonlinear differential equation [20,26,27,36,37]. The solution of this equation for a suitable initial condition determines what has been, by abuse of terminology, called the "attractor solution."…”

Section: Setupmentioning

confidence: 99%

“…Previous works have focused on fluids undergoing Bjorken flow [20,26,27,36,37] and nonhomogeneous expanding plasmas [39]. We expand these studies by investigating the properties of the attractors in the plasmas undergoing Gubser flow [40,41].…”

Section: Introductionmentioning

confidence: 99%

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

2018

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The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

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“…Another possibility is the entropy equation (with a non-vanishing source term, as entropy must grow in non-equilibrium situations) [27]. But in principle, also higher moments of the Boltzmann equation could serve to determine the anisotropy parameter [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

2016

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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,f 0k , 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 fromf 0k . Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

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Anisotropic hydrodynamics for a mixture of quark and gluon fluids

Cited by 25 publications

References 45 publications

Mixture of Quark and Gluon Fluids Described in Terms of Anisotropic Hydrodynamics

Mixture of Quark and Gluon Fluids Described in Terms of Anisotropic Hydrodynamics

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

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