On the scaling approach to electron-electron interactions in a chaotic quantum dot

TL;DR

This paper develops a scaling theory to analyze how electron-electron interactions behave in a double quantum dot system, revealing that electron delocalization does not alter the fundamental interaction criteria.

Contribution

It introduces a scaling approach to understand electron interactions in coupled quantum dots, showing the universality of the interaction Hamiltonian despite electron delocalization.

Findings

Electron delocalization does not affect the instability criterion.

The universal interaction Hamiltonian remains valid in double quantum dots.

Scaling theory effectively describes low energy electron interactions.

Abstract

A scaling theory is used to study the low energy physics of electron-electron interactions in a double quantum dot. We show that the fact that electrons are delocalized over two quantum dots does not affect the instability criterion for the description of electron-electron interactions in terms of a ``universal interaction Hamiltonian''.