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Entropy production in a longitudinally expanding Yang–Mills field with use of the Husimi function: semiclassical approximation

Matsuda, Hidefumi Kunihiro, Teiji Ohnishi, Akira Takahashi, Toru T 京都大学 DOI:10.1093/ptep/ptac086

2022.07

概要

We investigate the possible thermalization process of the highly occupied and weakly coupled Yang–Mills fields expanding along the beam axis through an evaluation of the entropy, particle number, and pressure anisotropy. The time evolution of the system is calculated by solving the equation of motion for the Wigner function in the semiclassical approximation with initial conditions mimicking the glasma. For the evaluation of the entropy, we adopt Husimi–Wehrl (HW) entropy, which is obtained by using the Husimi function, a positive semidefinite quantum distribution function given by smearing the Wigner function. By numerical calculations at g = 0.1 and 0.2, the entropy production is found to occur together with the particle creation in two distinct stages: In the first stage, the particle number and entropy at low longitudinal momenta grow rapidly. In the second stage, the particle number and entropy of higher longitudinal momentum modes show a slower increase. The pressure anisotropy remains in our simulation and implies that the system is still out of equilibrium.

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our study agrees with the von Neumann entropy in the high-temperature and weak-coupling

limit.

Next, we show that the HW entropy defined by Eq. (20) takes the minimum value 1 for the

perturbative vacuum state as

= 1.

(D7)

SHW ({ω}) ≥ SHW ({ω})

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

PTEP 2022, 073D02

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