Entanglement Generation in the Scattering of One-Dimensional Particles

TL;DR

This paper introduces a framework to quantify entanglement generated during non-relativistic scattering of two particles in one dimension, highlighting the roles of momentum, mass, and interaction potential.

Contribution

It presents a new quantitative method and approximate formulas for evaluating entanglement in particle scattering, linking purity and momentum uncertainties.

Findings

Entanglement depends on initial momentum distributions, masses, and interaction potential.

Two scales, kinematic and dynamic, influence entanglement generation.

Derived formulas facilitate numerical evaluation of entanglement.

Abstract

This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter non-relativistically in one dimension. It explores how three factors determine the amount of entanglement generated: the momentum distributions of the incoming particles, their masses, and the interaction potential. Two important scales emerge, one set by the kinematics and one set by the dynamics. This method also provides two approximate analytic formulas useful for numerical evaluation of entanglement and reveals an interesting connection between purity, linear coordinate transformations, and momentum uncertainties.