Exact solution for the non-equilibrium attractor in number-conserving relaxation time approximation

Abstract

We extend previous studies of the conformal 0+1d kinetic non-equilibrium attractor in relaxation time approximation by enforcing number conservation through the introduction of a dynamical fugacity (chemical potential). We derive two coupled integral equations for the effective temperature and fugacity which are then solved numerically to obtain the exact solution. The resulting solutions exhibit convergence to a unique non-equilibrium attractor when the scaled moments of the distribution function are plotted as a function of the rescaled time w = tau/tau_eq. This occurs even though the system is out of chemical equilibrium at late times. In addition, compared to the case where number conservation was not imposed, we find that the moments converge to their respective attractors more quickly, particularly for moments with m=0. Finally, we compare the resulting attractor moments with predictions from different hydrodynamic frameworks.

arXiv comment19 pages, 5 figures

References in corpus (28)

• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma
• New theories of relativistic hydrodynamics in the LHC era
• Dissipative Dynamics of Highly Anisotropic Systems
• Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
• Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Influence of the shear viscosity of the quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions
• Fluid Dynamics far from Local Equilibrium
• Anisotropic flow in sqrt(s)=2.76 TeV Pb+Pb collisions at the LHC
• Extracting the QGP viscosity from RHIC data -- a status report from viscous hydrodynamics
• Anisotropic Hydrodynamics for Rapidly Expanding Systems
• Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
• Relativistic anisotropic hydrodynamics
• Holographic isotropization linearized
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Chemical Equilibration in Hadronic Collisions
• 3+1d quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions
• Components of the elliptic flow in Pb-Pb collisions at 2.76 TeV
• Measuring Quark-Gluon-Plasma Thermalization Time with Dileptons
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Anisotropic fluid dynamics
• Model-independent determination of the shear viscosity of a trapped unitary Fermi gas: Application to high temperature data
• Highly anisotropic hydrodynamics -- discussion of the model assumptions and forms of the initial conditions

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• Far-from-equilibrium attractors with Full Relativistic Boltzmann approach in 3+1 D: moments of distribution function and anisotropic flows $v_n$
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