论文标题
随机Schrödinger-lohe模型
Stochastic Schrödinger-Lohe model
论文作者
论文摘要
Schrödinger-lohe模型由与特定耦合的Schrödinger方程系统相互相互作用的波函数组成，使得所有波函数都在$ l^2 $单位球上演变。在过去的十年中，该模型已经进行了广泛的研究，并显示在初始状态的合适假设下，如果等待足够长的时间，所有的波函数都会彼此任意接近，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显示了该扰动模型的同步弱版本。
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.
