In this talk we discuss some recent results I obtained for a class of nonlinear models in quantum mechanics. In particular we focus our attention to the nonlinear one-dimensional Schrodinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark–Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs; for a detailed treatment we refer to Sacchetti (Phys Rev E 95:062212, 2017, SIAM J Math Anal 50(6):5783–5810, 2018) where this model has been studied.

中文翻译：

---

量子力学中的非线性模型和分叉树：近期研究进展

在本次演讲中，我们讨论了我从量子力学中的一类非线性模型获得的一些最新结果。特别是，我们将注意力集中在具有周期电势和Stark型摄动的非线性一维Schrodinger方程上。在大的周期性势的极限下，线性方程的斯塔克-旺尼尔梯形图成为一个密集的能谱，因为固定解的分歧出现了。有关详细处理，请参考Sacchetti（Phys Rev E 95：062212，2017，SIAM J Math Anal 50（6）：5783–5810，2018），其中已研究了该模型。