The Schrödinger-Lohe (SL) model is an infinite-dimensional non-Abelian generalization of
the Kuramoto model which serves as a prototype model for quantum synchronization. In this
paper, we study asymptotic behavior and the nonlinear stability problem for the SL model
with identical (one-body) potential. For this model, we show that there are only two possible
asymptotic states (the completely synchronized state or bi-polar state) emerging from
generic initial data, and the completely synchronized state and bi-polar state are nonlinearly …