Asymptotic behavior and stability for the Schrodinger-Lohe model

초록

The Schrodinger-Lohe (S-L) 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 S-L 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 stable and unstable, respectively. The restricted uniform L-2-stability is established with respect to constrained initial data on some invariant manifold. We also present the global existence and stability of standing wave solutions for the S-L model with a harmonic potential. Published by AIP Publishing.

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