Nonlinear charge and energy dynamics of an adiabatically driven interacting quantum dot

We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven interacting quantum dot in contact with a reservoir for arbitrary amplitudes of the driving potential. We study within this framework the Anderson impurity model with a local ac gate voltage. We show that the exact adiabatic quantum dynamics of this system is fully determined by the behavior of the charge susceptibility of the frozen problem. At $T=0$, we evaluate the dynamic response functions with the numerical renormalization group (NRG). The time-resolved heat production exhibits a pronounced feature described by an instantaneous Joule law characterized by a universal B\"uttiker resistance quantum R₀=h/(2e²) for each spin channel. We show that this law holds in the noninteracting as well as in the interacting system and also when the system is spin polarized. In addition, in the presence of a static magnetic field, the interplay between many-body interactions and spin polarization leads to a nontrivial energy exchange between electrons with different spin components.