Shear viscosity of a classical Yang-Mills field
Abstract
We investigate the shear viscosity η of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. Dependence of the shear viscosity η(g,T) on the coupling g and temperature T is represented by a scaling function fη(g2T) as η(g,T) = Tfη(g2T) due to the scaling-invariant property of the CYM. The explicit functional form of fη(g2T) is successfully determined from the calculated shear viscosity: It turns out that η(g,T) of the CYM field is proportional to 1/g1.10–1.88 at weak coupling, which is a weaker dependence on g than that in the leading-order perturbation theory but consistent with that of the “anomalous viscosity” η ∝ 1/g1.5 under the strong disordered field. The obtained shear viscosity is also found to be roughly consistent with that estimated through the analysis of the anisotropy of the pressure of the CYM dynamics in the expanding geometry with recourse to a hydrodynamic equation.
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); Japan Society for the Promotion of Science (JSPS)
- OSTI Identifier:
- 1734418
- Alternate Identifier(s):
- OSTI ID: 1849603
- Grant/Contract Number:
- FG02-05ER41367; 19K03872; 19H01898; 19H05151
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 11; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics; Dissipative dynamics; Transport phenomena; Relativistic heavy-ion collisions
Citation Formats
Matsuda, Hidefumi, Kunihiro, Teiji, Müller, Berndt, Ohnishi, Akira, and Takahashi, Toru T. Shear viscosity of a classical Yang-Mills field. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.102.114503.
Matsuda, Hidefumi, Kunihiro, Teiji, Müller, Berndt, Ohnishi, Akira, & Takahashi, Toru T. Shear viscosity of a classical Yang-Mills field. United States. https://doi.org/10.1103/PhysRevD.102.114503
Matsuda, Hidefumi, Kunihiro, Teiji, Müller, Berndt, Ohnishi, Akira, and Takahashi, Toru T. Mon .
"Shear viscosity of a classical Yang-Mills field". United States. https://doi.org/10.1103/PhysRevD.102.114503.
@article{osti_1734418,
title = {Shear viscosity of a classical Yang-Mills field},
author = {Matsuda, Hidefumi and Kunihiro, Teiji and Müller, Berndt and Ohnishi, Akira and Takahashi, Toru T.},
abstractNote = {We investigate the shear viscosity η of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. Dependence of the shear viscosity η(g,T) on the coupling g and temperature T is represented by a scaling function fη(g2T) as η(g,T) = Tfη(g2T) due to the scaling-invariant property of the CYM. The explicit functional form of fη(g2T) is successfully determined from the calculated shear viscosity: It turns out that η(g,T) of the CYM field is proportional to 1/g1.10–1.88 at weak coupling, which is a weaker dependence on g than that in the leading-order perturbation theory but consistent with that of the “anomalous viscosity” η ∝ 1/g1.5 under the strong disordered field. The obtained shear viscosity is also found to be roughly consistent with that estimated through the analysis of the anisotropy of the pressure of the CYM dynamics in the expanding geometry with recourse to a hydrodynamic equation.},
doi = {10.1103/PhysRevD.102.114503},
journal = {Physical Review D},
number = 11,
volume = 102,
place = {United States},
year = {Mon Dec 07 00:00:00 EST 2020},
month = {Mon Dec 07 00:00:00 EST 2020}
}
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