Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

TL;DR

This paper investigates resonance states in two-electron quantum dots using variational and complex scaling methods, focusing on entanglement, fidelity, and orthogonality to analyze state transitions and introduce complex entropy.

Contribution

It introduces a novel approach to calculating complex linear entropy for resonance states using complex scaling, and compares multiple methods for energy determination.

Findings

Linear entropy varies with electron repulsion near the resonance transition.

Fidelity and double orthogonality functions effectively identify resonance energies.

Complex linear entropy provides new insights into resonance state properties.

Abstract

Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the electron repulsion at both sides of the critical value, where the ground (bound) state becomes a resonance (unbound) state. The linear entropy and fidelity and double orthogonality functions are compared as methods for the determination of the real part of the energy of a resonance. The complex linear entropy of a resonance state is introduced using complex scaling formalism.