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The hydrodynamic attractors paradigm aims to explain the applicability of hydrodynamics after a very short timescale in ultra-relativistic nuclear collisions at RHIC and LHC in terms of the emergence of universal behavior across different…

High Energy Physics - Theory · Physics 2025-08-25 Michal P. Heller , Clemens Werthmann

The hydrodynamic attractor is a concept that describes universal equilibration behavior in which systems lose microscopic details before hydrodynamics becomes applicable. We propose a setup to observe hydrodynamic attractors in ultracold…

Quantum Gases · Physics 2025-06-18 Keisuke Fujii , Tilman Enss

Whether, how, and to what extent solutions of Bjorken-expanding systems become insensitive to aspects of their initial conditions is of importance for heavy-ion collisions. Here we study 1+1D and phenomenologically relevant boost-invariant…

High Energy Physics - Phenomenology · Physics 2020-03-18 Aleksi Kurkela , Wilke van der Schee , Urs Achim Wiedemann , Bin Wu

Understanding how hydrodynamics emerges rapidly in the medium produced by relativistic heavy-ion collisions remains a key theoretical challenge. While the attractor solution -- manifesting as a non-thermal fixed point during the early…

Nuclear Theory · Physics 2025-09-12 Shile Chen , Shuzhe Shi

Hydrodynamic attractors have recently gained prominence in the context of early stages of ultra-relativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of…

High Energy Physics - Theory · Physics 2020-09-24 Michal P. Heller , Ro Jefferson , Michał Spaliński , Viktor Svensson

Hydrodynamic attractors are a universal phenomenon of strongly interacting systems that describe the hydrodynamic-like evolution far from local equilibrium. In particular, the rapid hydrodynamization of the Quark-Gluon Plasma is behind the…

Quantum Gases · Physics 2026-03-17 Aleksas Mazeliauskas , Tilman Enss

Non-conformal attractor behavior is studied by solving non-conformal second order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and…

Nuclear Theory · Physics 2022-03-14 Zenan Chen , Li Yan

The nonequilibrium evolution in a boost-invariant Bjorken flow of a hybrid viscous fluid model containing two interacting components with different viscosities, such that they represent strongly and weakly self-coupled sectors, is shown to…

High Energy Physics - Phenomenology · Physics 2021-01-04 Toshali Mitra , Sukrut Mondkar , Ayan Mukhopadhyay , Anton Rebhan , Alexander Soloviev

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with a constant shear viscosity relaxation time. We…

Nuclear Theory · Physics 2018-04-04 Gabriel S. Denicol , Jorge Noronha

We analytically investigate hydrodynamic attractor solutions in both M\"{u}ller-Israel-Stewart (MIS) and kinetic theories in a viscous fluid system undergoing a Hubble expansion with a fixed expansion rate. We show that the gradient…

Nuclear Theory · Physics 2021-09-29 Zhiwei Du , Xu-Guang Huang , Hidetoshi Taya

We exploit the concept of hydrodynamic attractors to establish a general relation between the initial state energy and the produced particle multiplicities in high-energy nuclear collisions. When combined with an ab initio model of energy…

High Energy Physics - Phenomenology · Physics 2021-01-01 Giuliano Giacalone , Aleksas Mazeliauskas , Sören Schlichting

We study universal features of the hydrodynamization process in heavy-ion collisions using QCD kinetic theory simulations for a wide range of couplings. We introduce the new concept of limiting attractors, which are obtained by…

High Energy Physics - Phenomenology · Physics 2025-06-25 Kirill Boguslavski , Aleksi Kurkela , Tuomas Lappi , Florian Lindenbauer , Jarkko Peuron

A review of the recent progress of relativistic hydrodynamic attractors is presented, with a focus on applications in heavy ion collisions and the quark gluon plasma. Pedagogical introductions to the effective descriptions relevant for…

High Energy Physics - Theory · Physics 2022-04-27 Alexander Soloviev

We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously…

High Energy Physics - Phenomenology · Physics 2023-07-14 Huda Alalawi , Michael Strickland

"Attractor" solutions for the pre-hydrodynamic, far-from-equilibrium, evolution of the matter produced in relativistic heavy ion collisions have emerged as crucial descriptors of the rapid hydrodynamization of quark-gluon plasma (QGP).…

High Energy Physics - Phenomenology · Physics 2025-04-22 Krishna Rajagopal , Bruno Scheihing-Hitschfeld , Rachel Steinhorst

Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high…

High Energy Physics - Theory · Physics 2018-01-19 Paul Romatschke

We derive a first-order, stable and causal, relativistic hydrodynamic theory from the microscopic kinetic equation using the gradient expansion technique in a general frame. The general frame is introduced from the arbitrary matching…

Nuclear Theory · Physics 2022-07-27 Rajesh Biswas , Sukanya Mitra , Victor Roy

We derive the general analytical solution of the viscous hydrodynamic equations for an ultrarelativistic gas of hard spheres undergoing Bjorken expansion, taking into account effects from particle number conservation, and use it to…

Nuclear Theory · Physics 2020-04-22 Gabriel S. Denicol , Jorge Noronha

A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…

Fluid Dynamics · Physics 2007-05-23 Edsel A. Ammons

A very early start up time of the hydrodynamic evolution is needed in order to reproduce observations from relativistic heavy-ion collisions experiments. At such early times the systems is still not locally equilibrated. Another source of…

Nuclear Theory · Physics 2009-04-24 P. Bozek
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