Random-matrix approach to time-dependent forcing in many-body quantum systems

Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a recently proposed nonlinear response theory which is based on typicality and random-matrix methods, and which is applicable to a wide variety of such parametrically perturbed systems in and out of equilibrium: We derive analytical approximations of the characteristic response function for the two limiting cases of fast driving and of strong and short-ranged-in-energy driving. Furthermore, we work out implications and predictions for common applications, including finite-time quenches and time-dependent forcing that breaks conservation laws of the underlying undriven system. Finally, we verify all predictions by numerical examples and discuss the theory's scope and limitations.