Nonlinear Schroedinger-Poisson Theory for Quantum-Dot Helium

TL;DR

This paper develops a nonlinear Schroedinger-Poisson model for two electrons in a quantum dot, capturing their interactions and electrostatics, and offers insights into quantum-classical transition and eigenstate properties.

Contribution

It introduces an effective nonlinear Schroedinger-Poisson framework that accounts for dimensional mismatch and eigenstate non-orthogonality in quantum-dot helium.

Findings

Model agrees with previous numerical results

Provides a simple approach for quantum-classical transition

Highlights properties due to eigenstate non-orthogonality

Abstract

We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the dimensional mismatch of the two-dimensional electronic system and the three-dimensional electrostatics. The results agree with earlier numerical calculations performed in a large basis of two-body states and provide a simple model for continuous quantum-classical transition with increasing nonlinearity. Specific intriguing properties due to eigenstate non-orthogonality are emphasized.