Time dependence of quantum entanglement in the collision of two particles

TL;DR

This paper investigates how quantum entanglement develops over time during a scattering event between two distinguishable particles interacting via a delta potential, providing an analytic approximation for the entanglement dynamics.

Contribution

It introduces an approximate analytic formula for the asymptotic two-particle wave function, capturing the entanglement evolution in a delta potential scattering scenario.

Findings

Derived an approximate formula for the asymptotic wave function.

Calculated the time dependence of the Neumann entropy.

Demonstrated entanglement emergence during particle collision.

Abstract

We follow the emergence of quantum entanglement in a scattering event between two initially uncorrelated distinguishable quantum particles interacting via a delta potential. We calculate the time dependence of the Neumann entropy of the one-particle reduced density matrix. By using the exact propagator for the delta potential, we derive an approximate analytic formula for the asymptotic form of the two-particle wave function which is sufficiently accurate to account for the entanglement features of the system.