Entropy production and isotropization in Yang–Mills theory using a quantum distribution function

Hidekazu Tsukiji,Teiji Kunihiro,Akira Ohnishi,Toru T Takahashi

doi:10.1093/ptep/ptx186

Hidekazu Tsukiji, Teiji Kunihiro + Show 2 more

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https://doi.org/10.1093/ptep/ptx186

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Abstract

We investigate thermalization process in relativistic heavy ion collisions in terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang-Mills field theory with the phenomenological initial field configuration known as the McLerran-Venugopalan model in a non-expanding geometry, which has instabilty triggered by initial field fluctuations. HW-entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov-Sina\"i rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around $1$ fm/c in the present calculation in the non-expanding geometry.

Highlights

A new form of matter consisting of deconfined quarks and gluons is formed in high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [1,2,3,4,5].The created matter is opaque for colored particles, shows hydrodynamical behavior and collectivity of quarks, and decays into hadrons
We prove that the semiclassical time evolution dose not break the gauge invariance of the HW entropy
We show the calculated results of the Lyapunov exponents in the SU(2) Yang–Mills theory and show that the Lyapunov exponents are proportional to ε1/4, where ε is the energy density

Summary

Introduction

A new form of matter consisting of deconfined quarks and gluons is formed in high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [1,2,3,4,5].The created matter is opaque for colored particles, shows hydrodynamical behavior and collectivity of quarks, and decays into hadrons. A new form of matter consisting of deconfined quarks and gluons is formed in high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [1,2,3,4,5]. It is considered to be a quark gluon plasma (QGP). The early thermalization problem remains as a serious problem in high-energy heavy-ion collisions [8]. Hydrodynamical model analyses suggest that the created matter becomes close to local equilibrium at τth = 0.6–1.0 fm/c after the first contact, and this thermalization time is significantly shorter than the perturbative QCD estimate [9,10]

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