能谱涨落统计特征稳定性分析

通过引入权重,并用一能级数等于简并谱的无趋向性序列为标准去衡量 简并邻间距谱的趋向性,由此建立分析简并谱涨落统计特征稳定性的MKS无参量试验法;根 据该方法,具体分析、比较了H2O分子低激发态与高激发态振动能谱涨落统计特征,找出 了从低激发态向高激发态过度时涨落统计特征明显改变点。     

三原子分子体系振动能谱的涨落统计特征

文中对一系列三原子分子模型体系的振动能量本征值谱进行了涨落统计分析，探讨了组成原子质量和键角因素对能谱涨落统计特征的影响及规律。计算结果表明，折合质量的增大，键角的减小等分子结构特征，都将导致能谱结构混沌化程度的增高。     

三原子分子体系振能谱的涨落统计特征

文中对一系列三原子分子模型体系的振动能量本征值谱进行了涨落统计分析，探讨了组成原子质量和键角因素对能谱小组涨落统计特征的影响及规律。计算结果表明，折合质量的增大，键角的减小等分子结构特征，都将导致能谱结构混沌化程度的增高。     

IBFM模型U(6/4)超对称SO(6)极限的能谱统计

用相互作用玻色子费米子模型(IBFM)计算了奇A核U(6/4)超对称SO(6)极限的理论能谱，对不确定核的最近邻能级间距分布和能谱刚性度进行了研究，并对影响能谱统计特征的因素进行了讨论. 结果表明，有限的玻色子数N的大小显著地影响能谱统计. 当N接近于真实核的玻色子数时，子群SOBF(5)的作用强度和自旋对能谱统计起重要作用. 然而，当N趋于无穷大时，能谱统计总是趋于Poisson分布.     

C6H6可见光与红外跃迁强度的代数方法计算

在Iachello Oss的代数模型中 ,采用对称化基 ,利用在能谱计算中得到的分子的波函数的基础上 ,计算了C6H6和C6D6分子拉伸振动模式的可见光与红外跃迁强度 ,给出了拉曼跃迁的计算式 .跃迁算符的形式由分子对称性决定 .其中对称化基的构造 ,采用了对称化玻色表象方法 ,大大简化了计算 .计算结果与实验观测符合的相当好 .这表明其它振动模式与拉伸振动模式之间的耦合 ,或者很弱 ,或者可通过等效参数考虑进来 .研究表明 ,代数模型和对称化玻色表象方法的结合是解决分子振动问题的强有力的工具     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明: 有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的; 有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明:有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的;有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

基态6LiH和7LiD分子的精确Rydberg-RKR势能

本文将代数方法(AM;Sun et al,J.Mol.Spectrosc.2002,215:93)和Rydberg-Klein-Rees(RKR)方法相结合,获得了基态6Li H和7Li D同位素分子的高振动激发态能谱和Rydberg-RKR势能.所得势能产生的振动能谱同实验数据及AM结果均很好相符.这套方法可以用来有效研究分子内长程相互作用势.     

简并谱的涨落统计特征分析

通过引入权重的方式,使简并谱的积累函数形式上连续递增,并用带权重的多元线性拟合提取涨落谱,由此建立了一套适用于分析简并谱的ＮＮＳ分布、谱刚度、能谱分维函数等涨落统计特征的方法,并具体分析了Ｈ２Ｏ、ＮＨ３及ＣＨ４分子的振动能谱进行涨统计特征分析：发现它们的规则谱和约化非简并谱的涨落统计特征均已非Ｐｏｉｓｓｏｎ化;而且约化非简并谱的非Ｐｏｉｓｓｏｎ化程度较规则谱明显,即前者的能级斥力较后者大;此外,随     

C6H5COOH⋯X分子间氢键的理论研究

在B3LYP/6-311++G(3df,2p)理论水平,计算研究C6H5COOH...X分子间氢键的理论研究(X=H2O, HCOH, CH3COCH3, NH3, CH2NH和HCN)氢键体系。获得氢键复合物稳定结构、氢键相互作用能、振动频率、热力学性质等。计算结果表明,C6H5COO—H...X体系存在较强的O—H...O与O—H...N红移氢键。C6H5COO—H...X氢键复合物气态分子的自发形成过程温度不同,C6H5COOH...NH3和C6H5COOH...CH2NH 体系在室温下能自发进行,其余二聚体要在低温下才能自发进行。     

Benford’s law: A Poisson perspective

Benford’s law is a counterintuitive statistical law asserting that the distribution of leading digits, taken from a large ensemble of positive numerical values that range over many orders of scale, is logarithmic rather than uniform (as intuition suggests). In this paper we explore Benford’s law from a Poisson perspective, considering ensembles of positive numerical values governed by Poisson-process statistics. We show that this Poisson setting naturally accommodates Benford’s law and: (i) establish a Poisson characterization and a Poisson multidigit-extension of Benford’s law; (ii) study a system-invariant leading-digit distribution which generalizes Benford’s law, and establish a Poisson characterization and a Poisson multidigit-extension of this distribution; (iii) explore the universal emergence of the system-invariant leading-digit distribution, couple this universal emergence to the universal emergence of the Weibull and Fréchet extreme-value distributions, and distinguish the special role of Benford’s law in this universal emergence; (iv) study the continued-fractions counterpart of the system-invariant leading-digit distribution, and establish a Poisson characterization of this distribution; and (v) unveil the elemental connection between the system-invariant leading-digit distribution and its continued-fractions counterpart. This paper presents a panoramic Poisson approach to Benford’s law, to its system-invariant generalization, and to its continued-fractions counterpart.     

On the fractal characterization of Paretian Poisson processes

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto’s law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of ‘fractal processes’ exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes–with respect to physical randomness-based measures of statistical heterogeneity–is characterized by exponential Poissonian intensities.     

页岩气中CH4-C2H6吸附-扩散分子动力学研究

本文采用巨正则蒙特卡洛(GCMC)和分子动力学(MD)模拟方法,对比分析了不同温度、压力和孔径对二元气体(CH4-C2H6)在K-伊利石中的吸附-扩散的影响.结果表明,在低压条件下,K-伊利石对C2H6的吸附能力大于CH4, C2H6优先吸附在K-伊利石孔隙表面.热力学因子随着孔径的增加而减小,C2H6的热力学因子大于...     

Quantitative assessment of reparameterized PM6 (rPM6) for hydrogen abstraction reactions

In the present study, the usability of semiempirical quantum mechanical methods for calculating bond dissociation energy (BDE) was investigated systematically. Density functional theory (DFT) methods with the B3LYP and B97-1 functionals were used for comparison. We introduced a new test set for BDE, called BDE200, which covers a wide range of compounds including large aromatic compounds. The use of BDE200 test set revealed that the accuracy of the methods studied was ordered from best to worst as: B97-1 > B3LYP > rPM6 >> PM7 > PM6 > AM1 > PM3. In addition to the improved accuracy of rPM6 for predicting BDE, it was found that rPM6 can provide a quantitative correlation between BDE values and reactivity. The rPM6 calculated activation enthalpies for C–H hydroxylation catalysed by the compound I of cytochrome P450 were proportional to the calculated and experimental C–H BDE values, in line with the results of previous DFT studies. We believe that rPM6 can help develop a database, for instance, for the determination of site of metabolism.     

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.     

Rh6G/氧化多孔硅复合膜的荧光光谱

为了发展性能良好的固体染料激光器,多孔介质中镶嵌激光染料是一种可行的途径。将氧化多孔硅作为基质材料,通过浸泡的方式将激光染料Rh6G嵌入其中,形成Rh6G/氧化多孔硅复合膜,对比研究了Rh6G在无水乙醇、多孔硅、多孔氧化硅中的荧光特性。结果表明,经高温氧化后,氧化多孔硅透明度提高,其荧光强度明显变弱,在复合膜中已检测不到其荧光行为。相比于在无水乙醇溶液中,在氧化多孔硅中Rh6G发射光谱的半峰全宽有所展宽,峰值波长略有红移,对称性大为提高,具有类似单体发光特性,这种现象与纳米孔对Rh6G的聚集程度的限制有关。     

About the non vanishing of boundary terms in correlation functions as origin of phase transitions. A microscopic proof of a Goldstone theorem in classical statistical mechanics

We give a general microscopic proof that the well known Goldstone theorem connected with spontaneous symmetry breaking in quantum statistical mechanics and quantum field theory has a counterpart in classical statistical mechanics. Our approach is mainly based on the replacement of commutators by Poisson brackets as infinitesimal generators of symmetries and on the Fourier transformed version of the so called Kubo-Martin-Schwinger property of equilibrium states. Especially we show that the phase transition is related to the non vanishing of certain boundary contributions in Poisson brackets which from the naive point of view should vanish.     

Li修饰的C$lt;sub$gt;6$lt;/sub$gt;分子对H$lt;sub$gt;2$lt;/sub$gt;O的吸附研究

采用密度泛函理论中的广义梯度近似研究C₆Li吸附H₂O分子并将之进行分解的催化过程. 几何优化发现：Li原子最稳定的吸附位置是位于C 原子顶位上方. 研究表明,第一个H₂O 分子吸附在C₆Li上需要克服1.77 eV的能量势垒,然后分解为H和OH且与Li原子成键. 当吸附第二个H₂O分子时,第二个H₂O分子需要克服1.2 eV的能量势垒分解为H和OH,其中H与Li原子上的H原子结合成H₂,OH则替代Li 原子上的H结合在Li原子上. 因此C₆Li 可以作为催化剂将H₂O分子进行分解得到H₂. 分析可知：C₆Li主要是通过Li原子与H₂O之间形成的偶极矩作用来吸附H₂O 分子,与C₆₀Li₁₂ 的储氢机制类似. 研究结果可为储氢材料的制备提供一个新的思路. 关键词： 6')" href="#">C₆ Li 2O')" href="#">H₂O 密度泛函理论     

Energy Level Statistics of the SO(6) Limit of Super-Symmetry U(6/4)in the IBFM

The energy levels of the SO(6) limit of super-symmetry U(6/4) belonging to odd-A nucleus are calculated with the interacting boson-fermion model. Its emphasis is to study the statistical properties of the nearest neighbor spacing distribution(NSD) and the spectral rigidity(△ ).And the factors that affect the properties of level statistics are also investigated. The calculated results indicate that the finite boson number N effect is prominent. When N has a value close to a realistic one, both the interaction strength of subgroup SOBF(5) and the spin play an important role in the energy level statistics. However, in the case of N close to infinite, the statistics all tend to be Poisson type.