标题: 在一简单流体内瞬间正则模之局域至非局域转变
Localization-Delocalization transition of the Instantaneous Normal Modes in a Simple Fluid
作者: 黄邦杰
Huang, Ban-Chiech
吴天鸣
Wu, Ten-Ming
物理研究所
关键字: 局域化-非局域化转变;瞬间正则模;有限尺度标度;普适性;多重碎形分析;能阶跨距分布;Localization-delocalization transition;instantaneous normal modes;finite-size scaling;level-spacing distribution;level-number variance;multifractal analysis;Andersion transition;truncated Lenneard-Jones potential;universality
公开日期: 2009
摘要: 在本文中,我们探讨在一简单短距交互作用流体内瞬间正则模之局域至非局域转变。此液体模型提供拓朴性无序系统的原形。在瞬间正则模频谱中,分别在正数与负数瞬间正则模频谱上发现转变点。我们使用有限尺度标度法定出转变点,并且计算关联长度的临界指数。在数值误差范围内,所估计的临界指数与安德森模型是一致的。此结果验证了三维的安德森模型与拓朴性无序系统的短距简单流体属于同样的统计普适性分类。
我们也对瞬间正则模做了多重碎形的分析。在局域与非局域转变的转变点附近,瞬间正则模表现出多重碎形的特性。用广义碎形维度与波分量强度频谱可以观测到在转变点上随着系统尺度的不变性。我们精确计算了波分量强度频谱,在转变点上,我们的结果与安德森模型有高度的一致性,证明了波分量强度频谱也是一个具有普适性的量。
In this thesis, we have investigated the localization-delocalization transitions (LDTs) of the instantaneous normal modes (INMs) in a simple□fluid with short-ranged interactions. The model□fluid is a prototype of topologically disordered systems. Two LDTs in the INM spectrum are found, and the locations are termed as the mobility edges (MEs) with one in the positive-eigenvalue branch and the other in the negative-eigenvalue one. The MEs and the critical exponents of the two LDTs are estimated
by the…finite-size scaling (FSS) for the second moments of the nearest-neighbor level-spacing (LS) distributions. Within numerical errors, the two estimated critical exponents are almost coincident with each other and close to that of the Anderson model (AM) in three dimensions. The
nearest-neighbor LS distribution at each ME is examined to be in a good agreement with that of the AM at the critical disorder. We conclud that the LDTs in the Hessian matrices of topologically disordered systems exhibit the critical behaviors of orthogonal universality class.
We also investigate the analysis of level-number variance (LNV) and level compressibility (LCP), which characterizes the nature of the correlation of energy levels beyond the mean LS.
Furthermore, in terms of the multifractal analysis, the INM eigenvectors exhibit a multifractal nature with the same generalized fractal dimensions and the sigularity spectrum. Our results indicate that the singularity spectrum of the multifractal INMs agrees with that of the AM at the critical disorder. This good agreement provides a numerical evidence for the universality of the multifractals at the localization-delocalization transition. With the multifractal INMs, we calculate the probability den-
sity funciton and the spatial correlation function of the squared vibrational amplitudes. With the multifractal INMs, the relation between the probability density function and the singularity spectrum is examined, so are the relations between the critical exponents of the spatial correlation
function and the generalized fractal dimensions.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079227803
http://hdl.handle.net/11536/40425
显示于类别:Thesis


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