Investigating interaction-induced chaos using time-dependent density functional theory

TL;DR

This paper explores how time-dependent density functional theory (TDDFT) can be used to study chaos induced solely by electron interactions in quantum systems, emphasizing the need to go beyond standard approximations.

Contribution

It demonstrates the potential of TDDFT to analyze interaction-induced chaos and discusses the limitations of the adiabatic approximation in this context.

Findings

TDDFT can access level-spacing statistics related to chaos.

Linear response in TDDFT reveals mechanisms of interaction-induced chaos.

Going beyond the adiabatic approximation is necessary for accurate results.

Abstract

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbour level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.