在一簡單液體之 INM 頻譜中尋找 Mobility Edge

Abstract

由於液體在粒子位置上的拓樸無序性，表達該液體位能面曲度的 Hessian 矩陣可視為一種亂數矩陣系集，在數學上與高斯正交系集 ( Gaussian orthogonal ensemble ) 近似。與歸類為晶格態無序模型的 Anderson model 比較，預期 Hessian 矩陣的本徵值頻譜有一 mobility edge 將整個頻譜分隔成侷限本徵模和延展本徵模兩段。在此論文中，我們將利用 level-spacing 分析，在 TLJ 簡單液體的正數本徵值頻譜中，決定 mobility edge 的位置。

Due to the topological disorder in particle positions of a liquid, the Hessian matrices, which characterize the curvatures of the potential energy surface of this liquid, can be considered as an ensemble of random matrices, similar as the Gaussian orthogonal ensemble in mathematics. Compared with the Anderson model, which is a disorder model in crystalline, the eigenvalue spectrum of the Hessian matrices is expected to have a mobility edge, which separates the full spectrum into the localized- and extended-eigenmode regions. In this thesis, we determine the mobility edge in the positive-eigenvalue spectrum of the TLJ simple fluid via the level-spacing analysis.