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Mauricio Martinez

Publications and source records attributed to Mauricio Martinez.

At least 37 records · Page 2Linked to original sources
arXiv2015

Investigating the domain of validity of the Gubser solution to the Boltzmann equation

We study the evolution of the one particle distribution function that solves exactly the relativistic Boltzmann equation within the relaxation time approximation for a conformal system undergoing simultaneously azimuthally symmetric transverse and boost-invariant longitudinal expansion. We show, for arbitrary values of the shear viscosity to entropy density ratio, that the distribution function can become negative in certain kinematic regions of the available phase space depending on the boundary conditions. For thermal equilibrium initial conditions, we determine numerically the physical boundary in phase space where the distribution function is always positive definite. The requirement of positivity of this particular exact solution restricts its domain of validity, and it imposes physical constraints on its applicability.

hep-ph↗
arXiv2015

Leading-order anisotropic hydrodynamics for central collisions

We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4 pi eta/s ~ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear viscosity to entropy density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4 pi eta/s in Israel-Stewart viscous hydrodynamics whereas in anisotropic hydrodynamics it has a maximum at 4 pi eta/s ~ 10. For all 4 pi eta/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.

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arXiv2015

Analytic solutions of the relativistic Boltzmann equation

We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second order hydrodynamics and fluid-gravity correspondence.

hep-th↗
arXiv2015

Nonconformal viscous anisotropic hydrodynamics

We generalize the derivation of viscous anisotropic hydrodynamics from kinetic theory to allow for non-zero particle masses. The macroscopic theory is obtained by taking moments of the Boltzmann equation after expanding the distribution function around a spheroidally deformed local momentum distribution whose form has been generalized by the addition of a scalar field that accounts non-perturbatively (i.e. already at leading order) for bulk viscous effects. Hydrodynamic equations for the parameters of the leading-order distribution function and for the residual (next-to-leading order) dissipative flows are obtained from the three lowest moments of the Boltzmann equation. The approach is tested for a system undergoing (0+1)-dimensional boost-invariant expansion for which the exact solution of the Boltzmann equation in relaxation time approximation is known. Nonconformal viscous anisotropic hydrodynamics is shown to approximate this exact solution more accurately than any other known hydrodynamic approximation.

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arXiv2014

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.

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arXiv2014

A 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 non-equilibrium dynamics is compared to 1st- and 2nd-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.

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arXiv2014

Coherence effects between the initial and final state radiation in a dense QCD medium

In these proceedings contribution we review our recent results of medium modifications to the coherence pattern between the initial and final state radiation. We study single gluon production off a highly energetic parton that undergoes a hard scattering and subsequently crosses a dense QCD medium of finite size. Multiple scatterings lead to a partial suppression of the interferences between different emitters that opens the phase space for large angle emissions. We briefly discuss the generalization of this setup to describe gluon production in the case of pA collisions by including finite length and energy corrections. The configuration studied here may have phenomenological consequences in high-energy nuclear collisions.

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arXiv2014

Non-boost-invariant anisotropic dynamics

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.

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arXiv2013

Coherence phenomena between initial and final state radiation in a dense QCD medium

In this work we investigate medium modifications to the interference pattern between initial and final state radiation. We compute single gluon production off a highly energetic parton that undergoes a hard scattering and subsequently crosses a dense QCD medium of finite size. We extend our previous studies obtained at first order in opacity by providing general results for multiple soft scatterings and their specific formulation within the harmonic oscillator approximation. We show that there is a gradual onset of decoherence between the initial and final state radiation due to multiple scatterings, that opens the phase space for large angle emissions. By examining the multiplicity of produced gluons, we observe a potentially large double logarithmic enhancement for dense media and small opening angles. This result points to a possible modification of the evolution equations due to a QCD medium of finite size. We briefly comment on the phenomenological consequences of this setup in high-energy nuclear collisions.

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arXiv2013

Anisotropic hydrodynamics -- basic concepts

Due to the rapid longitudinal expansion of the quark-gluon plasma created in relativistic heavy ion collisions, potentially large local rest frame momentum-space anisotropies are generated. The magnitude of these momentum-space anisotropies can be so large as to violate the central assumption of canonical viscous hydrodynamical treatments which linearize around an isotropic background. In order to better describe the early-time dynamics of the quark gluon plasma, one can consider instead expanding around a locally anisotropic background which results in a dynamical framework called anisotropic hydrodynamics. In this proceedings contribution we review the basic concepts of the anisotropic hydrodynamics framework presenting viewpoints from both the phenomenological and microscopic points of view.

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arXiv2012

Coherence and broadening effects in medium induced gluon radiation

Interferences between different emitters in the multi-parton shower is the building block of QCD jet physics in vacuum. The presence of a hot medium made of quarks and gluons is expected to alter this interference pattern. To study such effects, we derive the gluon emission spectrum off an "asymptotic quark" traversing a hot and dense QCD medium at first order in the medium density. The resulting induced gluon distribution gets modified when the new interference terms between the initial and final quark are included. We comment on the possible phenomenological consequences of this new contribution for jet observables in heavy-ion collisions.

hep-ph↗
arXiv2012

Interference between initial and final state radiation in a QCD medium

We investigate the color coherence pattern between initial and final state radiation in the presence of a QCD medium. We derive the medium-induced gluon spectrum of an "asymptotic" parton which suffers a hard scattering and subsequently crosses the medium. The angular distribution of the induced gluon spectrum is modified when one includes interference terms between the incoming and the outgoing parton at finite angle between them. The coherent, incoherent and soft limits of the medium-induced gluon spectrum are studied. In the soft limit, we provide a simple and intuitive probabilistic picture which could be of interest for Monte Carlo implementations. The configuration studied here may have phenomenological consequences in high energy nuclear collisions.

hep-ph↗
arXiv2012

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 which 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 lab-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity to entropy ratio, proper time, and impact parameter.

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arXiv2012

Soft gluon emission off a heavy quark revisited

An improved generalized suppression factor for gluon emission off a heavy quark is derived within perturbative QCD, which is valid for the full range of rapidity of the radiated gluon and also has no restriction on the scaled mass of the quark with its energy. In the appropriate limit it correctly reproduces the usual dead cone factor in the forward rapidity region. On the other hand, this improved suppression factor becomes close to unity in the backward direction. This indicates a small suppression of gluon emission in the backward region, which should have an impact on the phenomenology of heavy quark energy loss in the hot and dense matter produced in ultra-relativistic heavy-ion collisions.

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arXiv2010

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.

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arXiv2010

Matching pre-equilibrium dynamics and viscous hydrodynamics

We demonstrate how to match pre-equilibrium dynamics of a 0+1 dimensional quark gluon plasma to 2nd-order viscous hydrodynamical evolution. The matching allows us to specify the initial values of the energy density and shear tensor at the initial time of hydrodynamical evolution as a function of the lifetime of the pre-equilibrium period. We compare two models for the pre-equilibrium quark-gluon plasma, longitudinal free streaming and collisionally-broadened longitudinal expansion, and present analytic formulas which can be used to fix the necessary components of the energy-momentum tensor. The resulting dynamical models can be used to assess the effect of pre-equilibrium dynamics on quark-gluon plasma observables. Additionally, we investigate the dependence of entropy production on pre-equilibrium dynamics and discuss the limitations of the standard definitions of the non-equilibrium entropy.

hep-ph↗
arXiv2009

High-energy dileptons from an anisotropic quark-gluon plasma

We calculate leading-order dilepton yields from a quark-gluon plasma which 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. A phenomenological model for the proper time dependence of the parton hard momentum scale, p_hard, and the plasma anisotropy parameter, xi, is proposed. The model describes the transition of the plasma from a 0+1 dimensional collisionally-broadened expansion at early times to a 0+1 dimensional ideal hydrodynamic expansion at late times. We find that high-energy dilepton production is enhanced by pre-equilibrium emission up to 50% at LHC energies, if one assumes an isotropization/thermalization time of 2 fm/c. Given sufficiently precise experimental data this enhancement could be used to determine the plasma isotropization time experimentally.

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