Non-linear charge and energy dynamics of an adiabatically driven interacting quantum dot

TL;DR

This paper develops a comprehensive theory for the adiabatic charge and energy transport in interacting quantum dots, revealing universal Joule law behavior and complex spin-dependent energy exchange phenomena.

Contribution

It introduces a general framework for analyzing time-dependent transport in interacting quantum dots driven by arbitrary ac potentials, linking dynamics to charge susceptibility and employing NRG for exact results.

Findings

Heat production follows a universal Joule law with resistance quantum R_0.

The law applies to both interacting and non-interacting systems, including spin-polarized cases.

Spin polarization and magnetic fields induce non-trivial energy exchange between spins.

Abstract

We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven interacting quantum dot in contact to 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 an universal resistance quantum $R_0=h/(2 e^2)$ for each spin channel. We show that this law holds in non-interacting 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 non-trivial energy exchange between electrons with different spin components.