Written by: Stephen Hsu

Primary Source: Information Processing

New paper! We hypothesize that rapid growth of entanglement entropy between modes in the central region and other scattering degrees of freedom is responsible for fast thermalization in heavy ion collisions.

Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions (arXiv:1506.03696)

Chiu Man Ho, Stephen D. H. Hsu

Let A be subsystem of a larger system A∪B, and ψ be a typical state from the subspace of the Hilbert space H_AB satisfying an energy constraint. Then ρ_A(ψ)=Tr_B |ψ⟩⟨ψ| is nearly thermal. We discuss how this observation is related to fast thermalization of the central region (≈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.

An earlier blog post Ulam on physical intuition and visualization mentioned the difference between intuition for familiar semiclassical (incoherent) particle phenomena, versus for intrinsically quantum mechanical (coherent) phenomena such as the spread of entanglement and its relation to thermalization.

[Ulam:] … Most of the physics at Los Alamos could be reduced to the study of assemblies of particles interacting with each other, hitting each other, scattering, sometimes giving rise to new particles. Strangely enough, the actual working problems did not involve much of the mathematical apparatus of quantum theory although it lay at the base of the phenomena, but rather dynamics of a more classical kind—kinematics, statistical mechanics, large-scale motion problems, hydrodynamics, behavior of radiation, and the like. In fact, compared to quantum theory the project work was like applied mathematics as compared with abstract mathematics. If one is good at solving differential equations or using asymptotic series, one need not necessarily know the foundations of function space language. It is needed for a more fundamental understanding, of course. In the same way, quantum theory is necessary in many instances to explain the data and to explain the values of cross sections. But it was not crucial, once one understood the ideas and then the facts of events involving neutrons reacting with other nuclei.

This “dynamics of a more classical kind” did not require intuition for entanglement or high dimensional Hilbert spaces. But see von Neumann and the foundations of quantum statistical mechanics for examples of the latter.