I will begin by reviewing general results on the equilibration of isolated quantum systems, including sufficient conditions for equilibration and a discussion of the timescales of this equilibration process. I will then focus on new results on the dynamics of two-point correlation functions. These include conditions under which correlation functions factorize at late times, and bounds on their temporal fluctuations. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound holds for arbitrary systems, is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models. Our study extends to further classes of two-point functions such as the symmetrized ones and the Kubo function that appears in linear response theory.
