Exact treatment of planar two-electron quantum dots: effects of anharmonicity on the complexity

TL;DR

This paper provides an exact analysis of two-electron quantum dots with anharmonic confinement, revealing how anharmonicity and Coulomb interactions influence spectral properties and induce chaos.

Contribution

It introduces a method for exact matrix element representation in anharmonic quantum dots, capturing full Coulomb interactions and analyzing resulting spectral and classical chaos properties.

Findings

Anharmonic potential significantly alters spectral characteristics.

Coulomb interaction and anharmonicity lead to classical chaos.

Eigenstate localization correlates with classical phase space properties.

Abstract

Static properties of an anharmonic potential model for planar two-electron quantum dots are investigated using a method which allows for the exact representation of the matrix elements, including the full Coulombic electron - electron interaction. The anharmonic confining potential in combination with the interparticle Coulomb interaction affects the spectral properties of the system considerably as it implies total loss of separability of the system. Properties of the classical phase space, spectral measures of the chaoticity, as well as localization properties of the eigenstates corroborate this.