Mauricio Martinez

Dissipative Dynamics of Highly Anisotropic Systems

In this paper we present a method to improve the description of 0+1 dimensional boost invariant dissipative dynamics in the presence of large momentum-space anisotropies. We do this by reorganizing the canonical hydrodynamic expansion of the distribution function around a momentum-space anisotropic ansatz rather than an isotropic equilibrium one. At leading order the result obtained is two coupled ordinary differential equations for the momentum-space anisotropy and typical momentum of the degrees of freedom. We show that this framework can reproduce both the ideal hydrodynamic and free streaming limits. Additionally, we demonstrate that when linearized the differential equations reduce to 2nd order Israel-Stewart viscous hydrodynamics. Finally, we make quantitative comparisons of the evolution of the pressure anisotropy within our approach and 2nd order viscous hydrodynamics in both the strong and weak coupling limits.

Boost-Invariant (2+1)-Dimensional Anisotropic Hydrodynamics

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)-dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one that is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the laboratory-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity-to-entropy ratio, proper time, and impact parameter.

Non-boost-invariant anisotropic dynamics

Abstract We study the non-boost-invariant evolution of a quark–gluon plasma subject to large early-time momentum–space anisotropies. Rather than using the canonical hydrodynamical expansion of the distribution function around an isotropic equilibrium state, we expand around a state which is anisotropic in momentum space and parameterize this state in terms of three proper-time and spatial-rapidity dependent parameters. Deviations from the Bjorken scaling solutions are naturally taken into account by the time evolution of the spatial-rapidity dependence of the anisotropic ansatz. As a result, we obtain three coupled partial differential equations for the momentum–space anisotropy, the typical momentum of the degrees of freedom, and the longitudinal flow. Within this framework ( 0 + 1 ) -dimensional Bjorken expansion is obtained as an asymptotic limit. Finally, we make quantitative comparisons of the temporal and spatial-rapidity evolution of the dynamical parameters and resulting pressure anisotropy in both the strong and weak coupling limits.

New Exact Solution of the Relativistic Boltzmann Equation and its Hydrodynamic Limit

We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow (Gubser flow). The resulting exact nonequilibrium dynamics is compared to first and second order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. This novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

Pre-equilibrium dilepton production from an anisotropic quark-gluon plasma

We calculate leading-order dilepton yields from a quark-gluon plasma that has a time-dependent anisotropy in momentum space. Such anisotropies can arise during the earliest stages of quark-gluon plasma evolution due to the rapid longitudinal expansion of the created matter. Two phenomenological models for the proper-time dependence of the parton hard momentum scale,

Constraining relativistic viscous hydrodynamical evolution

{p}_{mathrm{hard}}

Measuring quark-gluon-plasma thermalization time with dileptons.

, and the plasma anisotropy parameter, ensuremath{xi}, are constructed that describe the transition of the plasma from its initial nonequilibrium state to an isotropic thermalized state. The first model constructed interpolates between 1+1 dimensional free streaming at early times and 1+1 dimensional ideal hydrodynamical expansion at late times. In the second model we include the effect of collisional broadening of the parton distribution functions in the early-time pre-equilibrium stage of plasma evolution. We find for both cases that for fixed initial conditions high-energy dilepton production is enhanced by pre-equilibrium emission. When the models are constrained to fixed final pion multiplicity the dependence of the resulting spectra on the assumed plasma isotropization time is reduced. Using our most realistic collisionally broadened model we find that high-transverse-momentum dilepton production would be enhanced by at most 40% at the Relativistic Heavy Ion Collider and 50% at the CERN Large Hadron Collider if one assumes an isotropization/thermalization time of 2 fm/

Soft gluon emission off a heavy quark revisited

c

Leading-order anisotropic hydrodynamics for central collisions

. Given sufficiently precise experimental data this enhancement could be used to determine the plasma isotropization time experimentally.