Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions

Abstract

Let $A$ be subsystem of a larger system $A \cup B$, and $ψ$ be a typical state from the subspace of the Hilbert space ${\cal H}_{AB}$ satisfying an energy constraint. Then $ρ_A(ψ)= {\rm Tr}_B | ψ\rangle \langle ψ|$ is nearly thermal. We discuss how this observation is related to fast thermalization of the central region ($\approx A$) in heavy ion collisions, where $B$ represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of $A$. Entanglement between the modes in $A$ and $B$ plays a central role: the entanglement entropy $S_A$ increases rapidly in the collision. In gauge-gravity duality, $S_A$ is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.