arXiv subjects

Ulrich W. Heinz

Publications and source records attributed to Ulrich W. Heinz.

At least 19 recordsLinked to original sources

arXiv2025

Exploring the fluid behavior in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$ with viscous anisotropic hydrodynamics

The applicability of hydrodynamics in small collision systems remains controversial due to the small size and short lifetime of the system. In this letter, we employ viscous anisotropic hydrodynamics (VAH), which incorporates large pressure anisotropies, to study the collectivity in p+p collisions at $\sqrt{s}=13 \mathrm{TeV}$.VAH provides a good description for $v_{2}\{2\}$ and $v_{3}\{2\}$ over a wide range of multiplicities and correctly reproduces the experimentally observed negative $c_{2}\{4\}$. Traditional second-order viscous hydrodynamics (VH), on the other hand, can describe the measurements, in particular the negative $c_{2}\{4\}$, only with model parameters for which the bulk of the evolution is characterized by large values of the shear Knudsen number. It also can not capture the large longitudinal/transverse pressure anisotropy during the early evolution. These demonstrate the failure of traditional viscous hydrodynamics in small collision systems and establish viscous anisotropic hydrodynamics as a more reliable framework to describe the bulk evolution and the observed anisotropic flow in p-p collisions at the LHC.

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arXiv2019

Hydrodynamics from free-streaming to thermalization and back again

We study the evolution of the Knudsen and Reynolds numbers in (0+1)-dimensionally expanding fluids with Bjorken symmetry for systems whose microscopic mean free path rises more quickly with time than usually assumed. This allows us to explore within a simple 1-dimensional model the transition from initially thermalizing to ultimately decoupling dynamics. In all cases studied the dynamics is found to be controlled by hydrodynamic attractors for both the Knudsen and Reynolds numbers whose trajectories undergo characteristic changes as the dynamics changes from thermalizing to decoupling.

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arXiv2019

Hydrodynamic flow in small systems, or: "How the heck is it possible that a system emitting only a dozen particles can be described by fluid dynamics?"

The "unreasonable effectiveness" of relativistic fluid dynamics in describing high energy heavy-ion and even proton-proton collisions are demonstrated and discussed. Several recent ideas of optimizing relativistic fluid dynamics for the specific challenges posed by such collisions will be presented, and some thoughts will be offered why the framework works better than originally expected. I will also address the unresolved question where exactly hydrodynamics breaks down, and why.

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arXiv2017

Optimized fluid dynamics for heavy ion collisions

The (viscous) anisotropic hydrodynamic approach, especially after perturbative inclusion of all residual viscous terms, has been shown to dramatically outperform viscous hydrodynamics in several simplified situations for which exact solutions exist but which share with realistic expansion scenarios the problem of large dissipative currents. We will report on the present status of applying viscous anisotropic hydrodynamics in a highly efficient simulation of the full three-dimensional quark-gluon plasma. Results from accelerated $3{+}1$-dimensional viscous hydrodynamic simulations using graphics processing units will be compared to the anisotropic frameworks.

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arXiv2016

Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

Relativistic fluid dynamics is a major component in dynamical simulations of the quark-gluon plasma created in relativistic heavy-ion collisions. Simulations of the full three-dimensional dissipative dynamics of the quark-gluon plasma with fluctuating initial conditions are computationally expensive and typically require some degree of parallelization. In this paper, we present a GPU implementation of the Kurganov-Tadmor algorithm which solves the 3+1d relativistic viscous hydrodynamics equations including the effects of both bulk and shear viscosities. We demonstrate that the resulting CUDA-based GPU code is approximately two orders of magnitude faster than the corresponding serial implementation of the Kurganov-Tadmor algorithm. We validate the code using (semi-)analytic tests such as the relativistic shock-tube and Gubser flow.

physics.comp-ph↗

arXiv2016

Initial state fluctuations in collisions between light and heavy ions

In high energy collisions involving small nuclei (p+p or x+Au collisions where x=p, d, or $^3$He) the fluctuating size, shape and internal gluonic structure of the nucleon is shown to have a strong effect on the initial size and shape of the fireball of new matter created in the collision. A systematic study of the eccentricity coefficients describing this initial fireball state for several semi-realistic models of nucleon substructure and for several practically relevant collision systems involving small nuclei is presented. The key importance of multiplicity fluctuations in such systems is pointed out. Our results show large differences from expectations based on conventional Glauber model simulations of the initial state created in such collisions.

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arXiv2016

Pre-equilibrium dynamics and heavy-ion observables

To bracket the importance of the pre-equilibrium stage on relativistic heavy-ion collision observables, we compare simulations where it is modeled by either free-streaming partons or fluid dynamics. These cases implement the assumptions of extremely weak vs. extremely strong coupling in the initial collision stage. Accounting for flow generated in the pre-equilibrium stage, we study the sensitivity of radial, elliptic and triangular flow on the switching time when the hydrodynamic description becomes valid. Using the hybrid code iEBE-VISHNU we perform a multi-parameter search, constrained by particle ratios, integrated elliptic and triangular charged hadron flow, the mean transverse momenta of pions, kaons and protons, and the second moment $\langle p_T^2\rangle$ of the proton transverse momentum spectrum, to identify optimized values for the switching time $τ_s$ from pre-equilibrium to hydrodynamics, the specific shear viscosity $η/s$, the normalization factor of the temperature-dependent specific bulk viscosity $(ζ/s)(T)$, and the switching temperature $T_\mathrm{sw}$ from viscous hydrodynamics to the hadron cascade UrQMD. With the optimized parameters, we predict and compare with experiment the $p_T$-distributions of $π$, $K$, $p$, $Λ$, $Ξ$ and $Ω$ yields and their elliptic flow coefficients, focusing specifically on the mass-ordering of the elliptic flow for protons and Lambda hyperons which is incorrectly described by VISHNU without pre-equilibrium flow.

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arXiv2016

Mode-coupling effects in anisotropic flow in heavy-ion collisions

Higher-order anisotropic flows in heavy-ion collisions are affected by nonlinear mode coupling effects. It has been suggested that the associated nonlinear hydrodynamic response coefficients probe the transport properties and are largely insensitive to the spectrum of initial density fluctuations of the medium created in these collisions. To test this suggestion, we explore nonlinear mode coupling effects in event-by-event viscous fluid dynamics, using two different models for the fluctuating initial density profiles, and compare the nonlinear coupling coefficients between the initial eccentricity vectors before hydrodynamic expansion and the final flow vectors after the expansion. For several mode coupling coefficients we find significant sensitivity to the initial fluctuation spectrum. They all exhibit strong sensitivity to the specific shear viscosity at freeze-out, but only weak dependence on the shear viscosity during hydrodynamic evolution.

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arXiv2016

Transient oscillations in a macroscopic effective theory of the Boltzmann equation

A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical degree of freedom is introduced at leading order that breaks local momentum isotropy. By replacing the deviation of the distribution function from this quasi-equilibrium state in terms of moments of the leading-order distribution and applying a systematic power counting scheme that orders the non-hydrodynamic modes by their microscopic time scales, a closed set of equations for the dynamical degrees of freedom is obtained. Truncating this set at the level of the slowest non-hydroynamic mode we find that it exhibits transient oscillatory behavior -- a phenomenon previously found only in strongly coupled theories, where it appears to be generic. In weakly coupled systems described by the Boltzmann equation, these transient oscillations depend on the breaking of local momentum isotropy being treated non-perturbatively at leading order in the expansion of the distribution function.

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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

Pre-equilibrium evolution effects on heavy-ion collision observables

In order to investigate the importance of pre-equilibrium dynamics on relativistic heavy-ion collision observables, we match a highly non-equilibrium early evolution stage, modeled by free-streaming partons generated from the Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) and Monte Carlo Glauber (MC-Glb) models, to a locally approximately thermalized later evolution stage described by viscous hydrodynamics, and study the dependence of final hadronic transverse momentum distributions, in particular their underlying radial and anisotropic flows, on the switching time between these stages. Performing a 3-parameter fit of the measured values for the average transverse momenta $\langle p_\perp \rangle$ for pions, kaons and protons as well as the elliptic and triangular flows of charged hadrons $v_{2,3}^\mathrm{ch}$, with the switching time $τ_s$, the specific shear viscosity $η/s$ during the hydrodynamic stage, and the kinetic decoupling temperature $T_\mathrm{dec}$ as free parameters, we find that the preferred "thermalization" times $τ_s$ depend strongly on the model of the initial conditions. MC-KLN initial conditions require an earlier transition to hydrodynamic behavior (at $τ_s \approx$ 0.13 fm/$c$) , followed by hydrodynamic evolution with a larger specific shear viscosity $η/s\approx$ 0.2, than MC-Glb initial conditions which prefer switching at a later time ($τ_s\approx$ 0.6 fm/$c$) followed by a less viscous hydrodynamic evolution with $η/s\approx$ 0.16. These new results including pre-equilibrium evolution are compared to fits without a pre-equilbrium stage where all dynamic evolution before the onset of hydrodynamic behavior is ignored. In each case, the quality of the dynamical descriptions for the optimized parameter sets, as well as the observables which show the strongest constraining power for the thermalization time, are discussed.

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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.

hep-ph↗

arXiv2014

Anisotropic flow of thermal photons as a quark-gluon plasma viscometer

We present state-of-the-art calculations of viscous photon emission from nuclear collisions at RHIC and LHC. Fluctuating initial density profiles are evolved with event-by-event viscous hydrodynamics. Momentum spectra of thermal photons radiated by these explosively expanding fireballs and their $p_T$-differential anisotropic flow coefficients $v_n(p_T)$ are computed, both with and without accounting for viscous corrections to the standard thermal emission rates. Viscous corrections to the rates are found to have a larger effect on the $v_n$ coefficients than the viscous suppression of hydrodynamic flow anisotropies. The benefits of taking the ratio of elliptic to triangular flow, $v_2/v_3$, are discussed, and the spacetime regions which contribute dominantly to the photon flow harmonics are identified. The directed flow $v_1$ of thermal photons is predicted for RHIC and LHC energies.

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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.

hep-ph↗

arXiv2014

Second-order (2+1)-dimensional anisotropic hydrodynamics

We present a complete formulation of second-order (2+1)-dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly. We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

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arXiv2014

Viscous hydrodynamics for strongly anisotropic expansion

A new formulation of second-order viscous hydrodynamics, based on an expansion around a locally anisotropic momentum distribution, is presented. It generalizes the previously developed formalism of anisotropic hydrodynamics (aHydro) to include a complete set of dissipative currents for which equations of motion are derived by solving the Boltzmann equation in the 14-moment approximation. By solving the vaHydro equations for a transversally homogeneous, longitudinally boost-invariant system ((0+1)-dimensional expansion) and comparing with the exact solution of the Boltzmann equation in relaxation-time approximation we show that vaHydro performs much better than all other known second-order viscous hydrodynamic approximations.

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arXiv2014

Electromagnetic fingerprints of the Little Bang

Measurements of thermal photons emitted from the rapidly expanding hot and dense medium ("Little Bang") formed in ultra relativistic heavy-ion collisions, and their current theoretical interpretation, are reviewed.

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