somewhere in time

下面是昨天给一个暑期学校同学回的邮件的主体部分。 

As you know, “Fermi level” is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics. Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy states. So at absolute zero they pack into the lowest available energy states and build up a “Fermi sea” of electron energy states. The Fermi level is the level at which the electron occupancy is 0.5 (or the highest filled level at 0 K).

So it is at the equal foot of your define. And at the other temperature, the $E_f=(E_{HOMO}+E_{LUMO})/2$. Relatively, at the 0K, the eletrons are localized at the HOMO downwards, so the $E_f=E_{HOMO}$.

But at the real system calculations, we do really not place the Fermi Level at the middle of the HOMO and LUMO, and a experiential parameter is set to.

今年6月26号出版的美国科学院院刊中一篇文章(PNAS, 104，10762)中对异性性接触网络是不是服从幂律分布关系又插了一脚。在第一部分，作者提出了目前文献中关于性接触网络是幂律还是其它的肥尾分布的争论，而且说明本文的目的是弄清楚性接触网络中的性伙伴的分布。

觉得他们对每个人的性接触概率是不一样的分析很有意思：第一，每个人的性吸引力是不一样的；第二，每个人对待性伙伴的情感的偏好以及乱交和卖淫的态度并不一致；第三，每个人受他的社会环境，宗教以及价值观的影响。另外，在动态社会中，他们还可以猎取新的性伙伴，具有更多性伙伴的人更能在这场游戏中获得更多的猎物，猎取新的性伙伴心理上的刺激，调情的技巧随着实践的不断提高都对获取更多的性伙伴有益。

另外个人觉得对择优机制的描述挺不错的。

The important question, discussed in connection with the Landauer resistance, is the origin of dissipation in this approach. Indeed, finite dc current at finite dc voltage means that the energy is permanently dissipated. On the other hand, we consider only elastic scattering, so that the energy can not be dissipated in the scattering process. This problem is closely related to the phenomena of the residual resistance at low temperature, caused by impurities. In both cases we should introduce some thermalisation. In the case of the transport between the equilibrium contacts, this puzzle is resolved quite easy, the energy is dissipated in the contacts, the details of the dissipation are not relevant. More precisely, the incoming from the contacts to the System particles are equilibrium distributed, while outgoing particles propagate into the contacts
and are thermalised here.

首先是关于石墨的，一年多以来，石墨引起了人们的极大关注，很多杰出的实验和理论工作冒出来的非常快，这可以从Science, Nature, Phys.Rev.Lett.，arXiv:cond-mat等上面可以初见端倪。石墨这个东西这么常见，最近才发现他一些比较令人兴奋的性质实在是比较奇怪。最近一篇文章（arXiv:0706.2968）将双极电荷密度起伏跟逾渗电流联系起来，并提出了用随机电阻器网络来分析电导对掺杂和无序的标度依赖，以及磁阻和移相率。

 其次是S.Kosov组关于利用哈密顿量中的自相似来研究纳米线中的单通道电荷输运性质（J.Chem.Phys. 124, 104703)。在文章中他们证实了在共振隧道范围内，单通道跃迁表现出依赖于纳米线的长度以及附带电子的能量的一种自相似行为。他们利用DFT理论计算了Na原子线的Transimission，验证了这种自相似行为。Y.Luo组提出的计算大纳米器件的导电能力的CIS方法似乎与此有点相似的地方。CIS方法能够计算10万个电子的体系，这种比较夸张的计算能力让很多人感到惊讶。

Mark Newman proposed an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions (arxiv:07070080).  The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any s. They apply results to networks with the three most commonly studied degree distributions — Poisson, exponential, and power-law — as well as to the calculation of cluster sizes for bond percolation on networks, which correspond to the sizes of outbreaks of SIR epidemic processes on the same networks. For the particular case of the power-law degree distribution, also they show that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms, but takes an exponential form when a giant component is present.

Chem.Phys.Lett. 400,336

Jun Jiang

We have applied the elastic-scattering Green
s function theory to study the coherent electron transportation processes in both metal–alkanedithiol–metal (gold–[S(CH2)nS]–gold, n = 8–14) and metal–alkanemonothiol–metal (gold–[H(CH2)nS]–gold, n = 8–14) at the hybrid density functional theory level. It is shown that the current decreases exponentially with the molecular length. At the low temperature limit the electron decay rate, b, for alkanedithiol junction is found to be around 0.30/CH2 at 1.0 V bias, much smaller than the calculated value of 0.60/CH2 for alkanemonothiol junction. The decay rate for alkanedithiol junction at the room temperature is neither sensitive to the activation of the Au–S stretching vibrational mode nor to the external bias. The calculated current–voltage characteristics and decay rates for both junctions are in excellent agreement with the corresponding experimental results.

Phys.Rev.B 71,165316

Z.Crljen

We theoretically study the electronic transport in the monolayer of dithiolated phenylene vinylene oligomeres coupled to the s111d surfaces of gold electrodes. We use nequilibrium Green’s functions and densityfunctional theory implemented in the TranSIESTA package to obtain a full ab initio self-consistent description of the transport current through the molecular nanostructure with different electrochemical bias potentials. The
calculated current-voltage characteristics of the systems for the same contact geometry have shown a systematic decrease of the conductivity with the increased length of the molecules. We analyze the results in terms of transmission eigenchannels and find that besides the delocalization of molecular orbitals the distance between gold electrodes also determines the transport properties.

Phys.Rev.B 75,245407:

Y.Zhou

In recent experiment it was found that for a quantum length dependence of conductance of oligothiophene-CH2 molecules under low bias [Xu et al., Nano Lett.5,1491],the longer molecule has larger conductance. Due to the experimental motivation, we calculated the conductance of a similar organic compound, oligothiophene, by means of the first-rinciples method. Our calculations show a similar quantum length dependence of conductance in the low bias region and an oscillated length dependence of conductance in the high bias region. The transport behaviors are determined by the distinct electronic structures of the molecular compounds. The length dependencies of conductance for several other oligomers are calculated to show the diversity in the transport behaviors of molecular wires. The results show that Ohm’s law is not valid for the molecular conductance anymore, and for the low bias region, Magoga’s law is not applicable for some
molecular wires, for example, oligothiophene dithiolates.

double-walled nanotubes(DWNTs) have attracted much attention during the past couple of years because of their novel structural and electronic properties compared to those multiwalled (MWNTs) and single-walled nanotubes (SWNTs).

 We (Dr.Jiang and I) got a interesting result on electronic transport of DWNTs. In these days, I prepare for the PPT and writing the paper, perhaps which will be submitted to Nano.Lett., and I will present some details in this Blog.

Duo to the unusual physical properties, carbon nanotubes have attracted lots of attentions. For the higher mechinical stiffness and greater thermal stability, double-walled nanotubes(DWNTs) may be have more benefit in field emission device comparing to single-walled nanotubes(SWNTs). Their double shell structure offers the possibility of shielding the inner tube for external perturbations. These merits make them very interesting for certain nano-device applications.

使用function是matlab中的一个很好的习惯，比如

function f=fibonacci(n)
这是第一行，function表明这是一个m文件，而不是命令脚本。第一行剩下的内容说明，这个函数有一个输出变量f，一个输入变量n。第一行中写的函数名其实并没有用，因为matlab使用m文件的名字，所以为使用方便通常应该使两个文件名字相同。下面通常还写上注释，并在使用help命令时显示出来。

比如我们前面四行如下：
function f=fibonacci(n)
% FIBONACCI Fibonacci sequence
% f=FIBONACCI generates the first n Fibonacci numbers.
f=zeros(n:1)

那么我们输入
help fibonacci
输出显示为
 FIBONACCI Fibonacci sequence
 f=FIBONACCI generates the firsr n Fibonacci numbers.

显示出的函数名是大写的，这是因为历史上matlab曾不区别大小写，且运行于只有一种字体的终端上。在注释中重复函数的输入，输出参数是很重要的，因为help命令的输出，不会函数文件第一行的内容。

I am reading this paper, and will write review here a week later.

Title :

Spin-dependent electronic structure of transition-metal atom chain adsorbed on single-wall carbon nanotubes