Thomas Epelbaum

Pressure isotropization in high energy heavy ion collisions.

The early stages of high energy heavy ion collisions are studied in the color glass condensate framework, with a real-time classical lattice simulation. When increasing the coupling constant, we observe a rapid increase of the ratio of longitudinal to transverse pressure. The transient regime that precedes this behavior is of the order of 1 fm/c.

Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow

Abstract Quantum fluctuations are believed to play an important role in the thermalization of classical fields in inflationary cosmology but their relevance for isotropization/thermalization of the classical fields produced in heavy ion collisions is not completely understood. We consider a scalar ϕ 4 toy model coupled to a strong external source, like in the Color Glass Condensate description of the early time dynamics of ultrarelativistic heavy ion collisions. The leading order classical evolution of the scalar fields is significantly modified by the rapid growth of time-dependent quantum fluctuations, necessitating an all order resummation of such “secular” terms. We show that the resummed expressions cause the system to evolve in accordance with ideal hydrodynamics. We comment briefly on the thermalization of the quantum system and the extension of our results to a gauge theory.

Role of quantum fluctuations in a system with strong fields: Spectral properties and thermalization

Abstract In a previous work [ arXiv:1009.4363 ], we have studied the evolution of a scalar field with a quartic coupling, driven by a classical source that initializes it to a non-perturbatively large value. At leading order in the coupling, the evolution of this system is given by classical solutions of the field equation of motion. However, this system is subject to a parametric resonance that leads to secular divergences in higher-order corrections to physical observables. We have proposed a scheme that resums all the leading secular terms: this resummation leads to finite results at all times, and we have observed also that it makes the pressure tensor of the system relax to its equilibrium value. In the present paper, we continue the study of this system by looking at finer details of its dynamics. We first compute its spectral function at various stages of the evolution, and we observe that after a fairly short transient time there are well-defined massive quasi-particles. We then consider the time evolution of the momentum distribution of these quasi-particles, and we show that after a stage dominated by the parametric resonance, this distribution slowly evolves to an equilibrium distribution. Interestingly, this distribution develops a transient chemical potential, signaling the fact that number changing processes are much slower than the elastic ones.

Fluctuations of the initial color fields in high energy heavy ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time

Instability induced pressure isotropization in a longitudinally expanding system

\tau \ll Q_s^{-1}

Nonrenormalizability of the classical statistical approximation

shortly after the collision, in the Fock-Schwinger gauge

Properties of the Boltzmann equation in the classical approximation

A^\tau=0

Isotropization of the quark gluon plasma

. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.

Initial state and thermalization

In two previous works [arXiv:1009.4363,arXiv:1107.0668], we studied the time evolution of a system of real scalar fields with quartic coupling which shares important features with the Color Glass Condensate description of heavy ion collisions. Our primary objective was to understand how such a system, when initialized with a non-perturbatively large classical field configuration, reaches thermal equilibrium. An essential goal of these works was to highlight the role played by the quantum fluctuations. However, these studies considered only a system confined within a box of fixed volume. In the present paper, we extend this work to a system that expands in the longitudinal direction thereby more closely mimicking a heavy ion collision. We conclude that the microscopic processes that drive the system towards equilibrium are able to keep up with the expansion of the system; the pressure tensor becomes isotropic despite the anisotropic expansion.

From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on

In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory. Although the ultraviolet power counting in this approximation scheme is identical to that of the unapproximated quantum field theory, this approximation is not renormalizable. The leading cause of this non-renormalizability is the breakdown of Weinbergs theorem in this approximation. We also discuss some practical implications of this negative result for simulations that employ this approximation scheme, and we speculate about a possible modification of the classical statistical approximation in order to systematically subtract the leading residual divergences.