On weak interaction between a ground state and a trapping potential

TL;DR

This paper investigates how a ground state interacts with trapping potentials under weak interaction conditions, analyzing the asymptotic behavior when the state moves away or is fast.

Contribution

It provides a detailed analysis of the asymptotic behavior of ground states interacting weakly with trapping potentials, which was not previously characterized.

Findings

Asymptotic behavior characterized for weak interactions

Ground state moves away from potential over time

Fast-moving ground states exhibit specific asymptotics

Abstract

We study the interaction of a ground state with a class of trapping potentials. We track the precise asymptotic behavior of the solution if the interaction is weak, either because the ground state moves away from the potential or is very fast.