The Schrödinger-Lohe model consists of wave functions interacting with each other, according to a system of Schrödinger equations with a specific coupling such that all wave functions evolve on the $L^2$ unit ball. This model has been extensively studied over the last decade and it was shown that under suitable assumptions on the initial state, if one waits long enough all the wave functions become arbitrarily close to each other, which we call a synchronization. In this paper, we consider a stochastic perturbation of the Schrödinger-Lohe model and show a weak version of synchronization for this perturbed model in the case of two oscillators.

中文翻译：

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随机薛定谔-洛厄模型

薛定谔-洛厄模型由相互作用的波函数组成，根据具有特定耦合的薛定谔方程组，所有波函数在 ${升}^2$单位球。该模型在过去十年中得到了广泛的研究，结果表明，在初始状态的适当假设下，如果等待足够长的时间，所有波函数就会变得任意接近，我们称之为同步。在本文中，我们考虑了 Schrödinger-Lohe 模型的随机扰动，并在两个振荡器的情况下展示了该扰动模型的弱同步版本。