Prescaling Relaxation to Nonthermal Attractors

Area of Science:

• Quantum physics
• Statistical mechanics
• High-energy physics

Background:

• Far-from-equilibrium quantum systems are crucial for understanding cold atoms and nuclear collisions.
• Nonthermal attractors represent a key theoretical concept in these systems.
• The dynamics of relaxation to these attractors are not fully understood.

Purpose of the Study:

• To investigate the relaxation dynamics of isotropic and homogeneous far-from-equilibrium quantum systems.
• To identify the mathematical framework governing the approach to nonthermal attractors.
• To analyze the impact of scaling-breaking terms on these dynamics.

Main Methods:

• Derivation of a first-order ordinary differential equation for prescaling.
• Analysis of logarithmically slow corrections due to scaling-breaking terms.
• Application of transseries as a mathematical structure for describing the dynamics.
• Verification using state-of-the-art 2PI simulations of the large-N vector model and QCD kinetic theory.

Main Results:

• A first-order ordinary differential equation accurately describes the self-similar approach (prescaling) to nonthermal attractors.
• Scaling-breaking terms introduce logarithmic corrections, hindering the attainment of constant scaling exponents.
• The transseries mathematical structure is proposed as suitable for describing these complex dynamics.
• Analytic predictions are validated by sophisticated numerical simulations.

Conclusions:

• The relaxation dynamics of far-from-equilibrium quantum systems towards nonthermal attractors are characterized by prescaling and logarithmic corrections.
• Transseries provide a robust mathematical framework for these dynamics, analogous to hydrodynamic attractors.
• This work offers new insights into quantum system evolution relevant to cold atom experiments and nuclear collisions.