Mass-transfer instability of ground-states for Hamiltonian Schr\"odinger systems

TL;DR

This paper investigates the orbital instability of ground-states in Hamiltonian Schrödinger systems, revealing a mass-transfer instability mechanism that leads to new instability results, especially for $L^2$-subcritical states.

Contribution

It introduces a general instability criterion for Hamiltonian Schrödinger systems with gauge invariance and applies it to demonstrate mass-transfer induced instability in various models.

Findings

Derived a new instability criterion for ground-states.

Identified mass-transfer instability as a key factor in orbital instability.

Exhibited unstable ground-states in $L^2$-subcritical regimes.

Abstract

We study generic semilinear Schr\"odinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange mass between them while preserving the total mass. We exploit this feature to unravel new orbital instability results for ground-states. More precisely, we first derive a general instability criterion and then apply it to some well-known models arising in several physical contexts. In particular, this mass-transfer instability allows us to exhibit $L^2$-subcritical unstable ground-states.