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arXiv:1309.4388 · Physical Review C

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions

S. V. Akkelin, Yu. M. Sinyukov

Published Mar 20, 2014• 9 citations

Abstract

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.

DOI: 10.1103/physrevc.89.034910

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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.

We show that the long wavelength modes of a field become classical during a second order phase transition because of the interaction with the short wavelength modes of the field. In a massive scalar field model the number and thermal states of long wavelength modes, whose Wigner functions are sharply peaked around the classical trajectories during the phase transition, exhibit only classical correlation without achieving quantum decoherence. In a linearly coupled scalar field model, the long wavelength modes are shown to effectively achieve quantum decoherence because of the mode mixing. Finally we define a quantal ordering parameter that is linear in the field variable and satisfies the classical field equation.

Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

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.