Effective thermal dynamics following a quantum quench in a spin chain

We study the nonequilibrium dynamics of the Quantum Ising Model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase coherence time ${\tau }_Q^{\varphi }$ from its asymptotic behavior. We show that the initial state determines ${\tau }_Q^{\varphi }$ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of ${\tau }_Q^{\varphi }$ on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.