N-particle scattering matrix for electrons interacting on a quantum dot

TL;DR

This paper derives a non-perturbative scattering matrix for N particles in a quantum dot, analyzing transmission and entanglement effects, providing a compact real-time formulation for complex interactions.

Contribution

It introduces a novel, non-perturbative expression for the N-particle scattering matrix in quantum dots, capturing resonance effects in a compact form.

Findings

Derived a non-perturbative scattering matrix for N particles.

Analyzed transmission probabilities and orbital entanglement.

Provided a real-time representation of the scattering process.

Abstract

We present a non-perturbative expression for the scattering matrix of $N$ particles interacting inside a quantum dot. Characterizing the dot by its resonances, we find a compact form for the scattering matrix in a real-time representation. We study the transmission probabilities and interaction-induced orbital entanglement of two electrons incident on the dot in a spin-singlet state.