Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-06-07
Physics
High Energy Physics
High Energy Physics - Phenomenology
29 pages, 18 figures, discussions on the non-linear regime and the power-law spectrum added, version accepted for publication
Scientific paper
We extensively study the growing behavior of the energy and the pressure components depending on the space-time rapidity in the framework of the Glasma, which describes the early-time dynamics in the ultra-relativistic heavy-ion collisions. We simulate the Glasma solving the classical equations of motion in the SU(2) Yang-Mills theory and systematically investigate the dependence of the Glasma instability on the model parameters. We have checked that the transverse and longitudinal grid sizes in our simulation are large enough to handle cutoff effects under control. By comparing the numerical results from several initial conditions with different magnitudes of instability seed and also those with different wave-numbers for rapidity fluctuations, we clearly see that unstable modes dominantly grow up in the linear regime and we also confirm non-linear effects in the time evolution. To extract more detailed information on the evolving Glasma, we decompose the energy into the components in terms of rapidity wave-numbers. We observe an energy flow from low wave-number modes into higher wave-number modes due to non-linearity in the equations of motion. We find that the energy spectrum approaches an asymptotic scaling that is consistent with Kolmogorov's power-law form even in the expanding system of the Glasma.
Fukushima Kenji
Gelis Francois
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