Late time dynamics of dynamical correlation functions and out of time ordered correlators

In this talk we study the universal properties of different types of dynamical quantites in time, for large classes of systems. First we investigate two-point correlation functions- also known as dynamical response functions in closed non-integrable many-body quantum systems. We show that for a large class of models these correlation functions factorize at late time, proving dissipation emerges from unitary dynamics. We similarly show that the fluctuations around the late time are bounded by the purity of the thermal ensemble. For auto-correlation functions we provide an upper bound on the timescale for which they equilibrate to this late time factorization. We then move onto study the late time dynamics of fermionic models in the presence of disorder for out of time ordered correlators. Focusing on the Aubry-André model we derive universal late time behavior for the OTOC in the extended regime of the model. These fermionic results are then used to extend the discussion to equilibration in finite time for all quadratic models in the extended regime.