Speaker
Description
We measure the Lyapunov exponent in SU(2) gauge theory under both in and out-of-thermal equilibrium conditions to understand the chaotic nature of non-Abelian gauge theories and its implications. Very close to the deconfinement temperature $T_c$, we use the fact that $SU(2)$ gauge theory falls within the same universality class as a $Z_2$ scalar field theory and calculate the Lyapunov exponent using out-of-time-ordered correlation (OTOC) function constructed out of the scalar fields. On the other hand in a high temperature ($T>>T_c$) thermal plasma, where the hard, electric and magnetic scales are well separated, we measure the Lyapunov exponent within the effective Hamiltonian theory of the soft gauge fields (magnetic modes). For measuring the degree of chaoticity from the Lyaponov exponent we consider a particular out-of-equilibrium state of SU(2) which describes a classical fixed point of the Hamiltonian evolution of the gauge fields and exhibit self-similar scaling. Such a state is obtained through classical evolution of gauge fields whose infrared momentum modes are over-occupied, and shows similar separation of hard and soft scales similar to a thermal plasma. We show that such a state is also chaotic. By calculating the Lyapunov exponent in this non-equilibrium state and comparing with its corresponding values at similar energy density in a thermalized SU(2) plasma we provide an estimate of the equilibration time. Our study can provide some insights about the thermalization time of the non-Abelian plasma formed in the heavy-ion collisions.
