论文标题
toeplitz矩阵$ e^{ - κ| i-j |} $及其应用于分层电子气体
The Toeplitz matrix $e^{- κ|i-j|}$ and its application to a layered electron gas
论文作者
论文摘要
我们提出了特定解决方案的特定解决方案，其中具有$ 0 \ leq i，j \ leq n $的特征toeplitz $ c_ {ij} = e^{ - κ| i-j |} $，并将其应用于分析中，以查找2同期电子气体的等离子体模式。通过基本方法找到该解决方案，即绕过通常用于此类问题的Wiener-HOPF技术。它基于这样的观察，即$ c_ {ij} $的倒数实际上是一个最近的邻居跳跃模型，具有特定的现场能量，又可以轻松地对角度化。在本文的末尾讨论了toeplitz和hankel矩阵的结合以及$ c_ {ij} $的概括的扩展。
We present an explicit solution of the eigen-spectrum Toeplitz matrix $C_{ij}= e^{- κ|i-j|}$ with $0\leq i,j \leq N$ and apply it to find analytically the plasma modes of a layered assembly of 2-dimensional electron gas. The solution is found by elementary means that bypass the Wiener-Hopf technique usually used for this class of problems. It rests on the observation that the inverse of $C_{ij}$ is effectively a nearest neighbor hopping model with a specific onsite energies which can in turn be diagonalized easily. Extensions to a combination of a Toeplitz and Hankel matrix, and to a generalization of $C_{ij}$, are discussed at the end of the paper.
