Prescaling relaxation to nonthermal attractors

TL;DR

This paper investigates how far-from-equilibrium quantum systems relax to nonthermal attractors, revealing a differential equation governing prescaling, the impact of scaling-breaking terms, and proposing transseries as the mathematical framework, supported by simulations.

Contribution

It introduces a differential equation model for prescaling to nonthermal attractors and highlights the role of logarithmic corrections, supported by simulations in quantum models.

Findings

A first-order ODE describes the approach to nonthermal attractors.

Scaling-breaking terms cause slow, logarithmic corrections.

Simulations confirm the analytic predictions.

Abstract

We study how isotropic and homogeneous far-from-equilibrium quantum systems relax to nonthermal attractors, which are of interest for cold atoms and nuclear collisions. We demonstrate that a first-order ordinary differential equation governs the self-similar approach to nonthermal attractors, i.e., the prescaling. We also show that certain natural scaling-breaking terms induce logarithmically slow corrections that prevent the scaling exponents from reaching the constant values during the system's lifetime. We propose that, analogously to hydrodynamic attractors, the appropriate mathematical structure to describe such dynamics is the transseries. We verify our analytic predictions with state-of-the-art 2PI simulations of the large-N vector model and QCD kinetic theory.