Quantum Synchronization for Stochastic Schrodinger-Lohe Model

The Schrödinger–Lohe model is an infinite-dimensional non-Abelian generalization of the Kuramoto model, which is brought up as an effective model for the study of quantum synchronization. In the Schrödinger–Lohe model, different wave functions interact with each other, which may lead to all the wave functions becoming arbitrarily close to each other after a long time under appropriate conditions. This phenomenon is called quantum synchronization. In this paper, we consider the Schrödinger–Lohe model perturbed by two kinds of multiplicative Gaussian white noises, and study the well-posedness and asymptotic behavior of the stochastic Schrödinger–Lohe models. Finally, we provide a weak quantum synchronization for the stochastic Schrödinger–Lohe model for the first case.