Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies (1303.5650v2)

Abstract: The non-equilibrium evolution of heavy-ion collisions is studied in the limit of weak coupling at very high energy employing lattice simulations of the classical Yang-Mills equations. Performing the largest classical-statistical simulations to date, we find that the dynamics of the longitudinally expanding plasma becomes independent of the details of the initial conditions. After a transient regime dominated by plasma instabilities and free streaming, the subsequent space-time evolution is governed by a nonthermal fixed point, where the system exhibits the self-similar dynamics characteristic of wave turbulence. This allows us to distinguish between different kinetic scenarios in the classical regime. Within the accuracy of our simulations, the scaling behavior found is consistent with the ``bottom-up" thermalization scenario.

Turbulent Thermalization Process in Heavy-Ion Collisions at Ultrarelativistic Energies

The paper of the non-equilibrium dynamics of quark-gluon plasma and its pathway to thermalization presents a persistent challenge in the field of quantum chromodynamics (QCD). The interplay of varied energy scales coupled with the complexities introduced by the non-Abelian nature of the gauge interactions underpins this unresolved problem. The paper under discussion investigates these dynamics by deploying lattice simulations of the classical Yang-Mills equations, focusing on the weak coupling limit at ultrarelativistic energies. The research employs and extends classical-statistical methods and tests for emergence of turbulent behavior and subsequent thermalization in scenarios characteristic of heavy-ion collisions.

The paper conducts the largest ever classical-statistical simulations to date in this domain, revealing that the plasma dynamics becomes independent of initial conditions after a transient period. This transient phase initially experiences dominance by plasma instabilities and free streaming, thereby leading to a regime exhibiting self-similar dynamics indicative of wave turbulence. The research aligns these observations with the nonthermal fixed point hypotheses and self-similarity paradigms explored in wave turbulence theories. Moreover, the paper demonstrates consistency within the scaling behavior of the system and the "bottom-up" thermalization scenario previously proposed by Baier, Mueller, Schiff, and Son (BMSS).

Numerical Methodology and Results

The extensive numerical simulations focus on a longitudinally expanding non-Abelian plasma, framed by the Yang-Mills problem formulated for the SU(2) gauge group in three spatial dimensions plus one time dimension. Key observables, such as the transverse $\Lambda_T$ and longitudinal $\Lambda_L$ hard momentum scales alongside pressure anisotropies, are meticulously analyzed. The simulations show that while initial transient dynamics are susceptible to plasma instabilities, late-time behaviors tend to exhibit universal scaling independent of initial settings — a transformation to a self-similar attractor state is observed. The analysis of pertinent metrics supports the turbulent nature of the evolving plasma, identifying a decrease in longitudinal momentum scaling contrary to the free streaming hypothesis.

The paper extensively reevaluates kinetic theories in the context of the observed results and discovers convergence towards the bottom-up scenario, implying an elastic scattering dominated dynamics in the initial stages. This prevailing scenario suggests that small-angle elastic scatterings among high-occupancy quasi-particle excitations accurately define the transition from the classical regime towards later stages, where more complex interactions could contribute significantly.

Theoretical Implications and Future Directions

The implications of these findings are substantial both theoretically and within the scope of high-energy experimental physics. The identification of a turbulent attractor expands the theoretical framework regarding the universality of turbulent scaling laws and self-similarity in high-energy QCD systems, akin to the wave turbulence observed in scalar field theories and cold atomic systems. From a more practical standpoint, understanding these dynamics can potentiate enhanced interpretative clarity over experimental observations made in large collider environments like the LHC and RHIC.

Future research directions might include a closer examination of the weak to strong coupling transition, beyond the reach of this classical-statistical approach, and further scrutiny into radiative interactions at quantum scales. The potential existence of a postulated secondary turbulent regime driven by $2 \leftrightarrow 3$ scattering processes deserves exploration, especially in the quantum domain beyond classical exclusions. These guideposts speak to the continued validity and necessity for expansive simulations and potentially hybrid methods integrating quantum statistical approaches with quasi-particle kinetic theory.

In conclusion, the paper is a pivotal advancement in delineating the dynamical evolution pathways within QCD-regulated environments, providing a richer understanding of the complex phenomenology underlying heavy-ion collisions, and contributing to the intricate mosaic of plasma thermalization theories in ultrarelativistic collisions.