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arXiv:1807.04589 · Journal of Physics Conference Series

Quantum entanglement in the initial and final state of relativistic heavy ion collisions

R. Bellwied

Published Aug 1, 2018• 10 citations
arXivHTMLPDF

Abstract

The possibility of quantum entanglement leading to a seemingly thermal distribution of the initial partonic state that maps to the final hadronic state in the evolution of the deconfined phase generated in relativistic heavy ion collisions is discussed in the context of early thermalization and final state particle distributions obtained in experiments at RHIC and the LHC.

DOI
10.1088/1742-6596/1070/1/012001

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The possibility of quantum entanglement leading to a seemingly thermal distribution of the initial partonic state that maps to the final hadronic state in the evolution of the deconfined phase generated in relativistic heavy ion collisions is discussed in the context of early thermalization and final state particle distributions obtained in experiments at RHIC and the LHC.
We present thermodynamic entropy calculations based on charged particle multiplicity data from proton-proton collisions measured by ALICE at the LHC in comparison to entanglement entropy calculations based on initial state parton distributions. The relative agreement of these distributions can be quantified by studying their higher order cumulants. The commonalities between the initial and final state entropy suggest that entanglement could be a possible source for the seemingly thermal and collective behavior in small systems.
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical mechanisms work in the case of the scalar field model. We obtain the evolution equation for the Wigner function of a long-wavelength subsystem that describes its decoherence, isotropization, and approach to thermal equilibrium induced by interaction with short-wavelength modes. Our analysis supports the idea that decoherence, quantum-to-classical transition, and thermalization in isolated quantum systems are attributed to the experimental context, and are related to a particular procedure of decomposition of the whole quantum system into relevant and irrelevant from an observational viewpoint subsystems.
The thermalization of the particles produced in collisions of small objects can be achieved by quantum entanglement of the partons of the initial state as was analyzed recently in proton-proton collisions. We extend such study to Pb-Pb collisions and to different multiplicities of proton-proton collisions. We observe that, in all cases, the effective temperature is approximately proportional to the hard scale of the collision. We show that such a relation between the thermalization temperature and the hard scale can be explained as a consequence of the clustering of the color sources. The fluctuations of the number of parton states decrease with multiplicity in Pb-Pb collisions as long as the width of the transverse-momentum distribution decreases, contrary to the $p\text{\ensuremath{-}}p$ case. We relate these fluctuations to the temperature fluctuations by means of a Langevin equation for the white stochastic noise. We show that the multiplicity parton distribution for events with at least one hard parton collision is a $\mathrm{\ensuremath{\Gamma}}$ distribution. We use this result to compute the entanglement entropy, showing that the leading term is the logarithm of the number of partons, meaning that the nnn microstates are equally probable and the entropy is maximal. There is another contribution related to the inverse of the normalized parton number fluctuation, which at very high energy changes the behavior from lnnlnnlnn to lnnln\sqrt{n}lnn​.
Let [Formula: see text] be subsystem of a larger system [Formula: see text] and [Formula: see text] be a typical state from the subspace of the Hilbert space [Formula: see text] satisfying an energy constraint. Then [Formula: see text] is nearly thermal. We discuss how this observation is related to fast thermalization of the central region ([Formula: see text]) in heavy ion collisions (HIC), where [Formula: see text] represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of [Formula: see text]. Entanglement between the modes in [Formula: see text] and [Formula: see text] play a central role: the entanglement entropy [Formula: see text] increases rapidly in the collision. In gauge–gravity duality, [Formula: see text] is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.
The thermalization of quark gluon plasma created in relativistic heavy-ion collisions is a crucial theoretical question in understanding the onset of hydrodynamics, and in a broad sense, a key step to the exploration of thermalization in isolated quantum systems. Addressing this problem theoretically, in a first principle manner, requires a real-time, non-perturbative method. To this end, we carry out a fully quantum simulation on a classical hardware, of a massive Schwinger model, which well mimics QCD as it shares the important properties such as confinement and chiral symmetry breaking. We focus on the real-time evolution of the Wigner function, namely, the two-point correlation function, which approximates quark momentum distribution. In the context of the eigenstate thermalization hypothesis and the evolution of entropy, our solution reveals the emergence of quantum thermalization in quark-gluon plasma with a strong coupling constant, while thermalization fails progressively as a consequence of the gradually increased significance of quantum many-body scar states in a more weakly coupled system. More importantly, we observe the non-trivial role of the topological vacuum in thermalization, as the thermalization properties differ dramatically in the parity-even and parity-odd components of the Wigner function.
In a quantum field theory, apparent thermalization can be a consequence of entanglement as opposed to scatterings. We discuss here how this can help to explain open puzzles such as the success of thermal models in electron-positron collisions. It turns out that an expanding relativistic string described by the Schwinger model (which also underlies the Lund model) has at early times an entanglement entropy that is extensive in rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature Tτ=ħ/(2πkBτ), even in the absence of any scatterings.