Crossover from nonequilibrium to equilibrium behavior in the time-dependent Kondo model

We investigate the equilibration of a Kondo model that is initially prepared in a nonequilibrium state towards its equilibrium behavior. Such initial nonequilibrium states can, e.g., be realized in quantum-dot experiments with time-dependent gate voltages. We evaluate the nonequilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between nonequilibrium and equilibrium behavior as the nonequilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method, we extend these results to the experimentally relevant limit of small Kondo couplings.