Thermalization in Yang-Mills Classical Mechanics

Abstract

We use quartic oscillators system with two degrees of freedom to model Yang-Mills classical mechanics. This simple model explains qualitatively many features reported in lattice calculation of $(3+1)$ - dimensional classical Yang-Mills system. The largest Lyapunov exponent ($\lambda$) and the thermalization time were numerically evaluated. We also show, in our model, that $\lambda$ scales with 4th root of energy density. Here thermalization is due to relaxation phenomena associated with the color degrees of freedom. From the physical picture of thermalization, we speculate that the system with coherent fields (flux tubes) formed in relativistic heavy ion collisions can relax by chaos and the estimated thermalization time can be smaller than $1 fm/c$.