Parametric instability of classical Yang-Mills fields in a color magnetic background

Abstract: We investigate instabilities of classical Yang-Mills fields in a time-dependent spatially homogeneous color magnetic background field in a non-expanding geometry for elucidating the earliest stage dynamics of ultra-relativistic heavy-ion collisions. The background gauge field configuration considered in this article is spatially homogeneous and temporally periodic, and is alluded by Berges-Scheffler-Schlichting-Sexty (BSSS). We discuss the whole structure of instability bands of fluctuations around the BSSS background gauge field on the basis of Floquet theory, which enables us to discuss the stability in a systematic way. We find various instability bands on the $(p_z, p_T)$-plane. These instability bands are caused by parametric resonance despite the fact that the momentum dependence of the growth rate for $|\mathbf{p}| \leq \sqrt{B}$ is similar to a Nielsen-Olesen instability. Moreover, some of instability bands are found to emerge not only in the low momentum but also in the high momentum region; typically of the order of the saturation momentum as $|\mathbf{p}| \sim \sqrt{B} \sim Q_{\rm s}$.