Entanglement and fast quantum thermalization in heavy ion collisions

Abstract

Let A be subsystem of a larger system A ∪ B, and ψ be a typical state from the subspace of the Hilbert space HAB satisfying an energy constraint. Then ρA(ψ) = TrB|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 SA increases rapidly in the collision. In gauge-gravity duality, SA is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.The usual particle scattering description of thermalization in heavy ion collisions (HIC) considers individual scattering events for each degree of freedom (i.e., parton). These scattering events are implicitly assumed to be incoherent -largely independent of each other. In the standard kinetic theory picture, multiple scatterings of each parton, one after another, are required to bring their distribution to the high entropy thermal configuration. By the usual reasoning, a timescale larger than 1 fm is required in order for these multiple, successive scatterings to occur.However, nucleus by nucleus scattering in HIC is a case of coherent scattering of two objects, each with many internal degrees of freedom. We can, in principle, describe the evolution of the wave functional ψ of the entire two nucleus system from asymptotic separation at early times to some specific post-collision moment in time, such as τ ≈ 1 fm after the initial overlap of the two nuclei. The wave functional then describes a superposition of each possible set of interactions or scatterings of individual partons in the system. The bulk or macroscopic properties of the remnant post-collision system are determined by an average over this complex superposition. Only a fraction of the total number of degrees of freedom are in the central region of the collision. The density matrix describing its properties is obtained through a trace over the remainder of the complex state.Recent results in the foundations of quantum statistical mechanics suggest that the system can thermalize through the spread of entanglement (i.e., superposition) much faster than expected from the usual (incoherent) kinetic theory. That is, the system can evolve from a very atypical state (two heavy nuclei, each with large boost) to a more typical one (entangled superposition state) over a short timescale.Below, we discuss fast thermalization in HIC (i.e., on timescales of τ ≈ 1 fm or less) in relation to the complex nature of the entangled superposition state, and the resulting growth of entanglement entropy. To be precise, what requires explanation is not full thermalization of the central region A, but rather the weaker condition of isotropization so that a hydrodynamic description becomes approximately valid. At minimum, the stress tensor of the matter in A must assume a diagonal form in its rest frame. For an overvie...

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