Stochastic Schr\"odinger-Lohe model
Abstract
The Schr\"odinger-Lohe model consists of wave functions interacting with each other, according to a system of Schr\"odinger equations with a specific coupling such that all wave functions evolve on the 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 Schr\"odinger-Lohe model and show a weak version of synchronization for this perturbed model in the case of two oscillators.
Cite
@article{arxiv.2009.12837,
title = {Stochastic Schr\"odinger-Lohe model},
author = {Reika Fukuizumi and Leo Hahn},
journal= {arXiv preprint arXiv:2009.12837},
year = {2021}
}
Comments
28 pages, 1 figure, changes : fixed typos, corrected proof of Proposition 7 and removed remarks about hypoellipticity (which were incorrect)