Periodic Reporting for period 1 - FEATURE (Far-from-Equilibrium ATtractors at Ultra-Relativistic Energies)
Período documentado: 2023-10-01 hasta 2025-09-30
The goal of FEATURE is to better understand how hydrodynamic attractors emerge in theories at relativistically high energies and their interplay with known features of relativistic flows. Hydrodynamic attractors can be thought of simply in the analogy with the water cycle. Let's say you were interested in describing the motion of water in our environment from point A to B. It may be difficult to simulate the evolution of every single molecule of water directly. However, there are large attractors of water, rivers for example, which capture the behavior of a significant fraction of that water. Moreover, they are easily described by a simpler set of equations than in the case of treating each water drop alone.
In a similar vein, the evolution equations for matter at high energies are known: microscopically, they are the equations of quantum chromodynamics. These are complicated to evolve from first principles without simplifying assumptions. Luckily, it has been observed that an important part of the violent aftermath of the collision of lead or gold nuclei can be described by relativistic hydrodynamics. This was more surprising as hydrodynamics was found to work even when gradients were large, outside of the usual domain of hydrodynamics. How does hydrodynamics work outside of its naive domain of applicability?
The resolution to this tension was in part the discovery of hydrodynamic attractors, akin to rivers in the previous example. These particular solutions represent the system's approach to a theory described by hydrodynamics. Different initial conditions approach hydrodynamics at different times (tributaries can enter the river at different times), but it is almost guaranteed that some of the evolution will be described by the attractor. In this sense, the system seems to "forget" about its intial conditions.
Despite this important step, a number of questions remain. Earlier studies focused on highly symmetric situations, whereas FEATURE expanded the picture by developing new approaches and solutions in systems with richer symmetries. It also addressed open questions about how phase transitions or the strong magnetic fields generated after the collision affect the attractor structure.
FEATURE sits naturally within the broader effort to understand real-time QCD dynamics. This is a core objective of major European and international experimental programs, including ALICE at CERN and the upcoming FAIR facilities. These experiments rely on accurate theoretical modeling (including hydrodynamic) to interpret signals of the quark–gluon plasma, including phase transitions, thermalization and other effects. By advancing our understanding of hydrodynamic attractors and extending them to more realistic flow geometries, FEATURE supports this need directly. Improved modeling of extreme states of matter contributes to both the long-term goals of fundamental physics and the strategic development of theoretical tools used across high-energy research.
In a similar vein, the evolution equations for matter at high energies are known: microscopically, they are the equations of quantum chromodynamics. These are complicated to evolve from first principles without simplifying assumptions. Luckily, it has been observed that an important part of the violent aftermath of the collision of lead or gold nuclei can be described by relativistic hydrodynamics. This was more surprising as hydrodynamics was found to work even when gradients were large, outside of the usual domain of hydrodynamics. How does hydrodynamics work outside of its naive domain of applicability?
The resolution to this tension was in part the discovery of hydrodynamic attractors, akin to rivers in the previous example. These particular solutions represent the system's approach to a theory described by hydrodynamics. Different initial conditions approach hydrodynamics at different times (tributaries can enter the river at different times), but it is almost guaranteed that some of the evolution will be described by the attractor. In this sense, the system seems to "forget" about its intial conditions.
Despite this important step, a number of questions remain. Earlier studies focused on highly symmetric situations, whereas FEATURE expanded the picture by developing new approaches and solutions in systems with richer symmetries. It also addressed open questions about how phase transitions or the strong magnetic fields generated after the collision affect the attractor structure.
FEATURE sits naturally within the broader effort to understand real-time QCD dynamics. This is a core objective of major European and international experimental programs, including ALICE at CERN and the upcoming FAIR facilities. These experiments rely on accurate theoretical modeling (including hydrodynamic) to interpret signals of the quark–gluon plasma, including phase transitions, thermalization and other effects. By advancing our understanding of hydrodynamic attractors and extending them to more realistic flow geometries, FEATURE supports this need directly. Improved modeling of extreme states of matter contributes to both the long-term goals of fundamental physics and the strategic development of theoretical tools used across high-energy research.
The activities performed included:
-Development of analytical frameworks for identifying hydrodynamic attractors in systems with spontaneous symmetry breaking, magnetic fields and near phase transitions.
-Determination of attractor in systems with phase transitions, including two geometries relevant for heavy-ion collisions and in Friedmann–Lemaître–Robertson–Walker spacetime.
-Numerical implementation of relativistic flows using the first holographic implementation of Gubser flow.
-Analysis of attractors in a newly discovered flow geometry.
-Complementary computations of thermoelectric and magnetic transport coefficients and correlators using kinetic theory and holography.
-Stochastic-hydrodynamic simulations and analytic work to study soft-pion production near the chiral phase transition.
-Last but not least, an important component of the Fellowship is the two way transfer of knowledge between the researcher and the host institution. I received direct scientific and soft training, including a numerical course in Computational Fluid Dynamics in HLRS, project management courses at the University of Ljubljana and Slovenian language courses to name a few. I transferred knowledge locally via a series of talks at our local seminar and the journal club.
The outcomes of the actions:
-Numerical codes and holographic tools for studying flows with nontrivial symmetries.
-A consistent framework for quantifying attractor time in relativistic systems.
-Several published papers (8 at time of writing) in high impact international peer-reviewed journals, documenting the results of FEATURE.
-Development of analytical frameworks for identifying hydrodynamic attractors in systems with spontaneous symmetry breaking, magnetic fields and near phase transitions.
-Determination of attractor in systems with phase transitions, including two geometries relevant for heavy-ion collisions and in Friedmann–Lemaître–Robertson–Walker spacetime.
-Numerical implementation of relativistic flows using the first holographic implementation of Gubser flow.
-Analysis of attractors in a newly discovered flow geometry.
-Complementary computations of thermoelectric and magnetic transport coefficients and correlators using kinetic theory and holography.
-Stochastic-hydrodynamic simulations and analytic work to study soft-pion production near the chiral phase transition.
-Last but not least, an important component of the Fellowship is the two way transfer of knowledge between the researcher and the host institution. I received direct scientific and soft training, including a numerical course in Computational Fluid Dynamics in HLRS, project management courses at the University of Ljubljana and Slovenian language courses to name a few. I transferred knowledge locally via a series of talks at our local seminar and the journal club.
The outcomes of the actions:
-Numerical codes and holographic tools for studying flows with nontrivial symmetries.
-A consistent framework for quantifying attractor time in relativistic systems.
-Several published papers (8 at time of writing) in high impact international peer-reviewed journals, documenting the results of FEATURE.
An overview of the main results of the project are:
-First ever characterization of the hydrodynamic attractor in systems with spontaneous symmetry breaking. This was carried out in two geometries relevant for heavy-ion collisions, as well as in Friedmann–Lemaître–Robertson–Walker spacetime, relevant for the evolution of the early universe.
-The novel definition of attractor time, the time that a system is well described by an attractor before reaching late time non-universal behavior due to the presence of other non-hydrodynamic modes.
-First ever holographic theoretical formulation and numerical exploitation of Gubser flow, providing the first strongly coupled description of the hydrodynamic attractor with enhanced symmetries.
-First description of a hydrodynamic attractor in a recently discovered flow by the supervisor, prof. Grozdanov, describing a sharply localized droplet of fluid that propagates rapidly along the light cone, reminiscent of wounded nuclei in the CGC picture.
Additional results, which offered important preliminary support for FEATURE's broader conclusions, include:
-Analytic computation of thermoelectric transport coefficients and correlators in kinetic theory for massless/massive gases in the relaxation time approximation
-Computation of correlators in magnetohydrodynamics, along with a novel determination of transport coefficients from a microscopic holographic theory. These are important steps in determining attractor behavior in MHD.
-Demonstrated via lattice simulations and analytic computations in stochastic hydrodynamics the enhancement of soft pion production for systems undergoing the chiral phase transition, which partially explains the discrepancy between experimental measurements at ALICE and hydrodynamic codes without critical effects included.
To ensure further uptake and maximize the impact of these results, the next key steps include: extending attractor analyses to more realistic hydrodynamic simulations and further developing numerical tools capable of efficiently capturing attractor behaviour in expanding geometries. Additional theoretical work in holography and kinetic theory is necessary to determine higher order transport coefficients and the effect of critical dynamics. Finally, expanded collaboration with experimental groups will support the translation of these findings into improved modeling frameworks.
-First ever characterization of the hydrodynamic attractor in systems with spontaneous symmetry breaking. This was carried out in two geometries relevant for heavy-ion collisions, as well as in Friedmann–Lemaître–Robertson–Walker spacetime, relevant for the evolution of the early universe.
-The novel definition of attractor time, the time that a system is well described by an attractor before reaching late time non-universal behavior due to the presence of other non-hydrodynamic modes.
-First ever holographic theoretical formulation and numerical exploitation of Gubser flow, providing the first strongly coupled description of the hydrodynamic attractor with enhanced symmetries.
-First description of a hydrodynamic attractor in a recently discovered flow by the supervisor, prof. Grozdanov, describing a sharply localized droplet of fluid that propagates rapidly along the light cone, reminiscent of wounded nuclei in the CGC picture.
Additional results, which offered important preliminary support for FEATURE's broader conclusions, include:
-Analytic computation of thermoelectric transport coefficients and correlators in kinetic theory for massless/massive gases in the relaxation time approximation
-Computation of correlators in magnetohydrodynamics, along with a novel determination of transport coefficients from a microscopic holographic theory. These are important steps in determining attractor behavior in MHD.
-Demonstrated via lattice simulations and analytic computations in stochastic hydrodynamics the enhancement of soft pion production for systems undergoing the chiral phase transition, which partially explains the discrepancy between experimental measurements at ALICE and hydrodynamic codes without critical effects included.
To ensure further uptake and maximize the impact of these results, the next key steps include: extending attractor analyses to more realistic hydrodynamic simulations and further developing numerical tools capable of efficiently capturing attractor behaviour in expanding geometries. Additional theoretical work in holography and kinetic theory is necessary to determine higher order transport coefficients and the effect of critical dynamics. Finally, expanded collaboration with experimental groups will support the translation of these findings into improved modeling frameworks.