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Nonlinear adiabatic response of interacting quantum dots

We develop a generic method in Liouville space to describe the dissipative dynamics of coherent interacting quantum dots with adiabatic time dependence beyond linear response. We show how the adiabatic response can be related to effective quantities known from real-time renormalization group methods for stationary quantities. We propose the study of a generalized $RC$-time as a characteristic time scale. We apply the method to the interacting resonant level model and calculate the nonlinear adiabatic charge response to time-dependent gate voltages, tunneling barriers and Coulomb interaction. The generalized $RC$-time is found to acquire a unique form in all cases, in contrast to the capacitance and the charge relaxation resistance. We discuss the observability of the effects in molecular systems and cold atom setups.