Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

Abstract: Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions.

• The paper introduces resurgence theory to resummate divergent fluid dynamic expansions in far-from-equilibrium regimes.
• It demonstrates non-equilibrium attractors that capture universal thermalization behavior in heavy-ion collision simulations.
• The study integrates microscopic theories with advanced numerical solvers to improve modeling of quark-gluon plasma dynamics.

Overview of "Relativistic Fluid Dynamics In and Out of Equilibrium"

Introduction

The field of relativistic fluid dynamics has seen significant advancements over the past decade, particularly in the context of heavy-ion collisions. This paper by Romatschke and Romatschke provides a comprehensive review of both theoretical and numerical developments in relativistic fluid dynamics, focusing on non-equilibrium systems as encountered in nuclear collision experiments.

Theoretical Developments

1. Gradient Expansion and Resurgence: A pivotal theme in the paper is the divergence of the conventional fluid dynamic gradient expansion and the applicability of Borel resummation techniques. The authors elaborate on how resurgence theory can provide insights into the non-perturbative properties of fluid dynamics, extending its applicability to far-from-equilibrium regimes.
2. Non-Equilibrium Attractors: The discussion introduces the concept of hydrodynamic attractors, which offer a powerful framework for understanding the evolution of systems even when they are not near local thermal equilibrium. This concept has become crucial for identifying universal behavior in the thermalization process of strongly interacting systems.
3. Inclusion of Fluctuations: The authors highlight the importance of including thermal fluctuations in fluid dynamic simulations to account for the stochastic nature of interactions at the microscopic level. These fluctuations become especially relevant in describing the initial stages of heavy-ion collisions where the system is away from equilibrium.
4. Microscopic Theories and Their Relation to Fluid Dynamics: The paper discusses how different microscopic theories, ranging from kinetic theory to holographic techniques (gauge/gravity duality), provide essential insights into the transport properties of the quark-gluon plasma, a key state of matter studied in high-energy nuclear physics.

Numerical Simulations

The integration of theoretical advances into numerical simulations marks a significant portion of the review. Key aspects include:

• Initial Condition Modeling: Simulation of relativistic heavy-ion collisions starts with the modeling of initial conditions. The paper reviews various approaches, including Glauber and IP-Glasma models, which describe the spatial distribution of energy immediately after nuclear impact.
• Hydrodynamic Evolution: The authors cover the implementation of state-of-the-art numerical solvers capable of handling the complex dynamics of rapidly evolving systems. These solvers incorporate advanced algorithms that respect causality and stability constraints dictated by the underlying theory.
• Particle Production and Decoupling: The transition from hydrodynamic descriptions to particle-based simulations (e.g., through Cooper-Frye or other freeze-out prescriptions) is crucial for connecting simulations to experimental observables. The paper provides insights into how these transitions are handled in modern computational frameworks.

Results and Comparisons

In juxtaposing simulation results with experimental data from facilities like RHIC and LHC, the paper underscores the success of relativistic fluid dynamics in capturing the bulk characteristics of the quark-gluon plasma. Moreover, it highlights the challenges still faced in accurately modeling certain phenomena, such as anisotropic flow and jet quenching.

Implications and Future Directions

The research reviewed in this paper has profound implications for our understanding of QCD matter under extreme conditions. The continued development of both theoretical models and computational techniques will likely unlock further insights into the properties of the early universe and compact astrophysical objects like neutron stars. The paper suggests future work could focus on refining the accuracy of initial condition models, enhancing the understanding of non-equilibrium processes, and exploring new experimental observables sensitive to the limitations of current models.

In conclusion, the review by Romatschke and Romatschke serves as an essential resource for researchers in nuclear and high-energy physics, offering both a broad overview and a detailed analysis of the progress in relativistic fluid dynamics as it pertains to nuclear collision experiments.