Coupling relativistic viscous hydrodynamics to Boltzmann descriptions

Abstract

Models of relativistic heavy ion collisions typically involve both a hydrodynamic module to describe the high density liquid-like phase and a Boltzmann module to simulate the low density breakup phase which is gas-like. Coupling the prescriptions is more complicated for viscous prescriptions if one wants to maintain continuity of the entire stress-energy tensor and currents. Derivations for the viscosity for a gas are reviewed, which then lead to expressions for changes in the phase space occupation based on simple relaxation-time pictures of viscosity. These expressions are shown to consistently reproduce the non-equilibrium components of the stress-energy tensor. An algorithm for generating a Monte Carlo sampling of particles with which to initiate the Boltzmann calculations is also presented.

Dissipative hydrodynamics coupled to chiral fields

“…For example, in the context of Grad's quadratic ansatz that is usually employed at freeze-out, this occurs when the nonequilibrium correction to the distribution function is comparable-or exceeds-the equilibrium one. In the context of relativistic heavy-ion collisions numerous hydrodynamic simulations (usually with temperature-independent η/s) have shown that large enough means η/s ∼ 0.3-0.5 [10,13,50,75,[77][78][79][80]. For larger values of η/s it is not possible to match the predictions of hydrodynamic models to RHIC data.…”

Determining transport coefficients for a microscopic simulation of a hadron gas

“…The extent of the simulation in the transverse direction was confined to a radius of R = 40 fm, with an extra buffer distance set up to ensure that the existence of the boundary could not affect the particles with radius r < R during the finite time over which the cascade ran. The initial momentum distribution was modified to reproduce arbitrary initial π zz using the techniques of [43]. The distribution of the particles longitudinally was confined to spatial rapidities −η s,min < η < η smax , with cyclic boundary conditions to longitudinal boosts.…”

“…The initial momenta were chosen according to the prescription in [43]. This code was modified relative to previous versions to initially generate particles with a distribution of masses consistent with a thermal-weighted modified Lorentzian distribution.…”

Accounting for backflow in hydrodynamic-Boltzmann interfaces

“…However, because collisions between two tracer particles is neglected, the list of interactions is abbreviated and given in Eq. (13). For a collision between incoming particles whose momenta, position and charges are labeled by p 1 and p 2 while the outgoing particles are denoted by q 1 , · · · q M , the cascade must consider three cases.…”

“…Viscous corrections can be applied according to [13]. This involves transforming the momentum according to (in the rest frame)…”