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 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.
 一 緒論 1.1 亂數矩陣理論 1.2 Level 統計與參與數 1.3 Anderson 相變 二 模型 2.1 物理系統 2.2 瞬間正則模 2.3 H 和 K 之間的相似性 三 方法 3.1 分子動力模擬 3.2 本徵方程數值解 3.3 Unfolding 處理 3.4 有限尺度縮放法 四 結果 4.1 全頻譜檢測（正數區段） 4.2 部份頻譜檢測（相變點附近） 五 結論
 [1]M. L. Mehta, Random Matrices, 2nd, Academic, New York, 1990.[2]J. A. d''Auriac, J. M. Maillard, ''Random Matrix Theory in Lattice Statistical Mechanics", Physica A 321, pp. 325-333, 2003.[3]J. M. Ziman, Models of Disorder, chap. 8 and chap. 9, Cambridge, 1982.[4]R. I. Shklovskii, B. Shapiro, et al. ''Statistical of Spectra of Disordered Systems near the Metal-Insulator Transition", Phys. Rev. B 47, pp. 11487-11490, May 1993.[5]E. Hofstetter, M. Schreiber, ''Statistical Properties of the Eigenvalue Spectrum of the Three-Dimensional Anderson Hamiltonian", Phys. Rev. B 48, pp. 16979-16985, December 1993.[6]E. Hofstetter, M. Schreiber,''Relation between Energy-Level Statistics and Phase Transition and Its Application to the Anderson Model", Phys. Rev. B 49,pp. 14726-14729, May 1994.[7]I. K. Zharekeshev, B. Kramer, ''Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition", Phys. Rev. B 51, pp. 17239-17242, June 1995.[8]I. K. Zharekeshev, B. Kramer, ''Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition", Phys. Rev. Lett. 79, pp. 717-720, July 1997.[9]M. Canales, J. A. Padr\''{o}, ''Static and Dynamic Structure of Liquid Metals: Role of the Different Parts of the Interaction Potential", Phys. Rev. E 56, pp. 1759-1764, August 1997.[10]M. Canales, J. A. Padr\''{o}, ''Dynamic Properties of Lennard-Jones Fluids and Liquid Metals", Phys. Rev. E 60, pp. 551-558, July 1999.[11]G. Seeley, T. Keyes, ''Normal-Mode Analysis of Liquid-State Dynamics", J. Chem. Phys. 91, pp. 5581-5586, November 1989.[12]T. M. Wu, R. F. Loring, ''Phonons in Liquids: A Random Walk Approach", J. Chem. Phys. 97, pp. 8568-8575, December 1992.[13]T. M. Wu, W. J. Ma, S. F. Tsay, ''Potential Effects on Instantaneous Normal Modes of Liquids", Physica A 254, pp. 257-271, 1998.[14]S. Sastry, N. Deo, S. Franz, ''Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices", Phys. Rev. E 64, pp. 016305-1\textasciitilde 4, June 2001.[15]M. P. Allen, D. J. Tildesley, Computer Simulation of Liquid, sec. 3.2.1 and sec. 5.3.2, Oxford, New York, 1990.[16]R. B. Lehoucq, D. C. Sorensen, C. Yang, ''ARPACK Users'' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods'''', http://www.caam.rice.edu/software/ARPACK/, October 1997.[17]F. M. Gomes, D. C. Sorensen, ''ARPACK++: An object-oriented version of ARPACK eigenvalue package", http://www.ime.unicamp.br/\textasciitilde chico/arpack++/, May 2000.[18]J. W. Kantelhardt, A. Bunde, L. Schweitzer, ''Extended Fractons and Localized Phonons on Percolation Clusters", Phys. Rev. Lett. 81, pp. 4907-4910, November 1998.
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 1 液態鋰的動力學性質研究 2 Lennard-Jones流體之瞬間正則模頻譜內遷移邊界的多重碎形分析 3 Lennard-Jones流體之瞬間正則模頻譜內遷移邊界隨作用力範圍,溫度及密度之變化

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