Hydrodynamic Attractors in Phase Space

Area of Science:

• Nuclear Physics
• High-Energy Physics
• Statistical Mechanics

Background:

• Hydrodynamic attractors are key to understanding the early stages of ultrarelativistic heavy-ion collisions.
• Existing theories often focus on specific models, necessitating a broader phase space perspective.

Purpose of the Study:

• To critically examine hydrodynamic attractors from a phase space viewpoint.
• To connect attractors to the general phenomenon of dynamical dimensionality reduction.
• To generalize these concepts to higher-dimensional systems.

Main Methods:

• Phase space analysis of hydrodynamic attractors.
• Application of Principal Component Analysis (PCA) for dimensionality reduction.
• Adaptation of the slow-roll approximation for dynamical systems.
• Analysis of high-dimensional phase space data from the Boltzmann kinetic equation (in the relaxation time approximation).

Main Results:

• Hydrodynamic attractors are identified as a specific instance of dynamical dimensionality reduction in phase space.
• Principal Component Analysis effectively quantifies this dimensionality reduction.
• The slow-roll approximation is successfully adapted to describe attractor dynamics.
• Preliminary analysis demonstrates generalization to a 16-dimensional phase space.

Conclusions:

• The phase space perspective provides a unifying framework for understanding hydrodynamic attractors.
• Dynamical dimensionality reduction is a more general concept applicable to heavy-ion collisions.
• The developed methods offer a pathway to analyze complex, high-dimensional systems in kinetic theory.