Nonlinear adiabatic response of interacting quantum dots

TL;DR

This paper introduces a Liouville space method to analyze the nonlinear adiabatic dynamics of interacting quantum dots, revealing a universal generalized RC-time and its implications for quantum systems.

Contribution

It develops a novel approach in Liouville space for nonlinear adiabatic response, connecting it to real-time renormalization group methods and introducing a generalized RC-time.

Findings

The generalized RC-time has a universal form across different scenarios.

Nonlinear adiabatic charge response can be calculated for various time-dependent parameters.

The method's predictions are relevant for molecular and cold atom experiments.

Abstract

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.