Optimizing Schroedinger functionals using Sobolev gradients: Applications to Quantum Mechanics and Nonlinear Optics
Juan Jose Garcia-Ripoll, Victor M. Perez-Garcia
在本文中,我们研究了Sobolev梯度技术在最小化量子力学和非线性光学中与及时和困难的非线性问题相关的几个薛定谔功能的问题中的应用。 我们表明,这些梯度在最小化方法中作为传统选择下降方向的先决条件,并展示了一种计算上廉价的方法,使用离散傅里叶基础和快速傅里叶变换来获得它们。 我们表明,Sobolev预处理比传统技术提供了很大的融合改进,用于以最小的能量和固定状态寻找解决方案,并建议使用任意线性运算符对方法进行概括。
In this paper we study the application of the Sobolev gradients technique to the problem of minimizing several Schrödinger functionals related to timely and difficult nonlinear problems in Quantum Mechanics and Nonlinear Optics. We show that these gradients act as preconditioners over traditional choices of descent directions in minimization methods and show a computationally inexpensive way to obtain them using a discrete Fourier basis and a Fast Fourier Transform. We show that the Sobolev prec...
