Time dependence of quantum entanglement in the collision of two particles

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.