Quantum Thermalization via Travelling Waves

TL;DR

This paper uses Dynamical Mean-Field Theory to analyze quantum thermalization, revealing a ballistic thermalization front described by a FKPP-type equation, providing insights into how isolated quantum systems reach equilibrium.

Contribution

It introduces a novel framework using DMFT to model quantum thermalization via traveling wave equations, linking quantum dynamics with classical reaction-diffusion models.

Findings

Thermalization front moves ballistically in the model.

The FKPP-type equation accurately predicts the front's shape and velocity.

Full DMFT numerics match the theoretical predictions.

Abstract

Isolated quantum many-body systems which thermalize under their own dynamics are expected to act as their own thermal baths, thereby bringing their local subsystems to thermal equilibrium. Here we show that the infinite-dimensional limit of a quantum lattice model, as described by Dynamical Mean-Field theory (DMFT), provides a natural framework to understand this self-consistent thermalization process. Using the Fermi-Hubbard model as working example, we demonstrate that the emergence of a self-consistent bath thermalising the system is characterized by a sharp thermalization front, moving balistically and separating the initial condition from the long-time thermal fixed point. We characterize the full DMFT dynamics through an effective temperature for which we derive a travelling-wave equation of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type. This equation allows to predict the asymptotic shape of the front and its velocity, which match perfectly the full DMFT numerics. Our results provide a new angle to understand the onset of quantum thermalisation in closed isolated systems.