Stochastic Schr?dinger-Lohe model
Stochastic Schr?dinger-Lohe model
复制标题
随机薛定谔-洛赫模型
DOI：
10.1016/j.jfa.2021.109224
复制
发表时间：
2021
影响因子：
1.7
通讯作者：
Hahn Leo
中科院分区：
文献类型：
--
作者：
Fukuizumi Reika;Hahn Leo
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，使得所有波函数在L2单位球上演化。在过去的十年中，这个模型已经被广泛研究，并且表明，在对初始状态的适当假设下，如果等待足够长的时间，所有的波函数都会变得任意接近，我们称之为同步。在本文中，我们考虑了薛定谔-洛厄模型的随机扰动，并在两个振子的情况下，证明了这种扰动模型的弱同步。
Abstract 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.