Scaling at the chaos threshold in an interacting quantum dot

TL;DR

This paper investigates how many-electron Fock states in a quantum dot exhibit chaotic mixing due to two-body interactions, revealing two regimes with a crossover characterized by a specific scaling parameter.

Contribution

It provides numerical and analytical analysis of the transition between regimes of chaotic mixing in quantum dots, highlighting the role of the scaling parameter (E/g)ln g.

Findings

Two regimes of inverse participation ratio I in Fock space identified

Crossover region shows a maximum in a scaling function

Scaling parameter (E/g)ln g governs the transition

Abstract

The chaotic mixing by random two-body interactions of many-electron Fock states in a confined geometry is investigated numerically and compared with analytical predictions. Two distinct regimes are found in the dependence of the inverse participation ratio in Fock space I on the dimensionless conductance of the quantum dot g and the excitation energy E. In both regimes I>>1, but only the small-g regime is described by the golden rule. The crossover region is characterized by a maximum in a scaling function that becomes more pronounced with increasing excitation energy. The scaling parameter that governs the transition is (E/g)ln g.