Planckian bound on the local equilibration time

TL;DR

This paper rigorously establishes a universal lower bound on the local equilibration time in quantum many-body systems, linking it to the Planckian time scale and showing it applies broadly regardless of microscopic details.

Contribution

The authors formalize and prove a universal lower bound on local equilibration time based on analytic properties of thermal correlators, independent of microscopic specifics.

Findings

Bound applies universally to quantum many-body systems

Lower bound proportional to Planckian time $rac{ ext{hbar}}{T}$

Independent of quasiparticle existence or inelastic scattering

Abstract

The local equilibration time $\tau_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$. We formalize this conjecture by defining $\tau_{\rm eq}$ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound $\tau_{\rm eq} \geq \alpha \hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $\alpha $ depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.