非Hermitian矩阵的特征值：一种动态和迭代的方法—应用于截断的Swanson模型,Mathematical Methods in the Applied Sciences

当前位置： X-MOL 学术 › Math. Methods Appl. Sci. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

非Hermitian矩阵的特征值：一种动态和迭代的方法—应用于截断的Swanson模型
Mathematical Methods in the Applied Sciences ( IF 2.1 ) Pub Date : 2020-03-15 , DOI: 10.1002/mma.6317
Fabio Bagarello _{1,

2} , Francesco Gargano ₁

Affiliation

我们提出了两种不同的策略来查找给定的矩阵（不一定是厄米矩阵）的特征值和特征向量

一种

。我们的方法也适用于复杂特征值的情况，这使得该策略对于物理应用尤其是伪厄尔米特量子力学尤为有趣。我们首先考虑一种动力学方法，该方法基于一对根据矩阵定义的常微分方程

一种

及其伴随

{一种}^{†}

。然后，我们考虑所谓的幂方法的扩展，为此我们证明了一个不动点定理

一种 \neq {一种}^{†}

在确定特征值时很有用

一种

和

{一种}^{†}

。这两种策略适用于一些显式问题。特别是，我们计算了由最近提出的量子力学系统（截短的Swanson模型）产生的矩阵的特征值和特征向量，并检查了Hessenberg矩阵的一些渐近特征。

"点击查看英文标题和摘要"

Eigenvalues of non‐Hermitian matrices: A dynamical and an iterative approach—Application to a truncated Swanson model

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix

A

. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo‐Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix

A

and of its adjoint

A^{†}

. Then, we consider an extension of the so‐called power method, for which we prove a fixed point theorem for

A \neq A^{†}

useful in the determination of the eigenvalues of

A

and

A^{†}

. The two strategies are applied to some explicit problems. In particular, we compute the eigenvalues and the eigenvectors of the matrix arising from a recently proposed quantum mechanical system, the truncated Swanson model, and we check some asymptotic features of the Hessenberg matrix.

更新日期：2020-03-15

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南