Initial condition dependence and wave function confinement in the Schrödinger–Newton equation

Abstract

In this work we study the dynamics of the Schrodinger–Newton (SN) equation upon different choices of initial conditions. Setting up superpositions of Gaussian-like wave packages, a very rich behavior for the critical mass as a function of the parameters of the problem is observed. We find that, for certain values of the parameters, the critical mass is smaller than the critical mass for the system whose initial condition is a single Gaussian wave package, which was the situation previously investigated in the literature. This opens a possibility that more complex initial conditions could in fact produce a significant decrease in the value of the critical mass, which could imply that the SN approach could be tested experimentally. Our conclusions rely on both numerical and analytic estimates. Furthermore, a detailed numerical study is carried out in order to investigate finite-size effects on the simulations, refining earlier results already published. In order to facilitate the reproducibility of our results, a detailed description of our numerical methods has been included in the presentation.