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September 12 Gosh, if you call that a publication at allWilliam Barford and Xibai Xu Erratum: “Groundstate dispersion interaction between  -conjugated polymers”J. Chem. Phys. 129, 079901 (2008) http://link.aip.org/link/?JCPSA6/129/079901/1 March 16 The Beauty of Physics - Part 4
有两个公式看不清楚是什么，还请知道的大侠不吝赐教。 (1) 一个特殊的洛仑兹变换——推动 (Lorentz Boost)，可以看作时间轴和空间轴之间的旋转。
(2) 看不清楚是什么公式 :( (3) 爱因斯坦引力场方程(Einstein's Field Equation)，广义相对论中最重要的公式。等号左边是描述时空曲率的爱因斯坦张量(Einstein Tensor)，等号右边是作为重力场源的应力-能量张量 (Stress-Energy Tensor)。万有引力常数G和光速c都设为1。
(4) 列维-奇维塔联络 (Levi-Civita Connection)，可以看作微分在黎曼几何中的推广。其在坐标空间里的表达式是克氏符号(Christoffel Symbol)。
(5) 广义相对论里的测地线微分方程 (Geodesic Equation)，描述两点间的最短路程，当公式(3)中的联络为欧几里的空间中的克氏符号时，该方程描述的是一条直线。
(6) 真空中的麦克斯韦方程组 (Maxwell's Equations)，自上而下分别代表 (1) 电场有源 (2) 磁场无源 (3) 变化的磁场产生电场 (4) 变化的电场产生磁场。
(7) 牛顿第二运动定律 (Newton's Second Law)。
(8) 拉格朗日场的最小作用量原理 (Principle of Least Action)。量子场论的基础公式之一。
(9) 广义相对论里的能动张量的守恒 (Conservation of Energy-Momentum Tensor)。 (10) 真空中的电磁波波动方程 (Electromagnetic Wave equation)。
(11) 经典统计物理里的麦克斯韦-波尔兹曼分布 (Maxwell-Boltzmann Distribution)。
(12) 推广到任意维度的位置动量正则对易关系 (Canonical Commutation Relations)，海森堡测不准原理的一种表达。
(13) 量子力学中单个粒子的薛定谔方程 (Time-Dependent Schrödinger Equation)。
(14) 质子（由三个夸克q1, q2, q3组成）和电子对撞的费曼图 (Feymann Diagram of Proton-Electron Scattering)。
(15) 看不清楚是什么公式 :( (16) 规范对称群 (Gauge Symmetry Groups)，整个粒子物理标准模型就浓缩成这三个对称群！ September 30 Viva
September 15 I Have Handed in My DissertationI finally handed in my dissertation today. However my supervisor has asked me to do some further work next week so that the results will be ready for submission for publication. If that goes well, I will soon have a second paper under my name (even if not first authored). That's probably more than what many PhD students would have done, but the whole point is - I'm not doing PhD after all! Why do I need another publication? I just can't help laughing myself off.
The Exciton Model of Dispersion Forces in Conjugated Polymers
Abstract
The dispersion interactions between two parallel conjugated polymers is studied using the exciton model and the line-dipole approximation. The correction to the ground state energy, is found to scale as L^2 and 1/R^6 in the L<<R limit, where L is the polymer length and R the distance between the two polymers. The scaling behaviour in the L>>R limit is qualitatively different from London formula, as E ~ L and E ~ 1/R^5. A similar model is applied to estimated the screening of excited states. Due to the increased transition density dipole moments and decreased energy differences between excited states, the screening energy is much higher for higher excited states. It also results in a longer time scale for the electron-hole motion compared to the dielectric. Hence, while the screening of the lowest excited state is dispersion-like, it becomes solvation-like for higher excited states. The screening energy for the second excited state is 0.57eV for R=1d=2.8Å. This energy scales as 1/R^2 and converges for large L.
45 pages with 21 references.
August 20 更正!!!
May 04 Ab Initio Methods for Electron CorrelationThis is for nerds only...
An overview of modern ab initio methods to treat electron correlation effects in molecular structure theory. Actually this is one of my worst written essays - rushed, lack of details and coherence. Even though it took me more than a week to finish. Now I don't even bother to look at it again.
Click on the title to access full text (pdf)
Created with MiKTeX 2.5 and LEd January 29 The Interpretation of Quantum Mechanics虽然我的CV里写着“会使用LaTeX”，但是用它排版正式的论文这还是第一次。这次的效果很好——因该说是非常令人满意——LaTeX做的数学公式真是赏心悦目啊！绝对不是word这样的软件能做出来的！ May 05 ZT: Physical Theories as WomenAuthor: Simon Dedeo
0. Newtonian gravity is your high-school girlfriend. As your first encounter with physics, she's amazing. You will never forget Newtonian gravity, even if you're not in touch very much anymore.
1. Electrodynamics is your college girlfriend. Pretty complex, you probably won't date long enough to really understand her.
2. Special relativity is the girl you meet at the dorm party while you're dating electrodynamics. You make out. It's not really cheating because it's not like you call her back. But you have a sneaking suspicion she knows electrodynamics and told her everything.
3. Quantum mechanics is the girl you meet at the poetry reading. Everyone thinks she's really interesting and people you don't know are obsessed about her. You go out. It turns out that she's pretty complicated and has some issues. Later, after you've broken up, you wonder if her aura of mystery is actually just confusion.
4. General relativity is your high-school girlfriend all grown up. Man, she is amazing. You sort of regret not keeping in touch. She hates quantum mechanics for obscure reasons.
5. Quantum field theory is from overseas, but she doesn't really have an accent. You fall deeply in love, but she treats you horribly. You are pretty sure she's fooling around with half of your friends, but you don't care. You know it will end badly.
6. Cosmology is the girl that doesn't really date, but has lots of hot friends. Some people date cosmology just to hang out with her friends.
7. Analytical classical mechanics is a bit older, and knows stuff you don't.
8. String theory is off in her own little world. She is either profound or insane. If you start dating, you never see your friends anymore. It's just string theory, 24/7.
- - - - - - - -
Quite funny, isn't it?
 Here I have my own addition to the list:9. M-theory: You soon discover that string theory has several sisters. The youngest one, M-theory, is fatally-seductive, possessing the best quality of all her siblings. However, she is the most religious of them and you either become a follower or grow up to dislike her. February 06 Cosmology1. Introduction
1.1 Conventions in Cosmology:
1) Metric signature +,-,-,-, Greek spacetime indices guv, Latin space indices gij.
2) Natural units c=h-bar=kb=1, [Energy]=[Mass]=[Temperature]=[Length]-1=[Time]-1.
3) Astronomical units 1 parsec = 3.261 year. Use megaparsec.
1.2 The Expansion of the Universe:
The Cosmological Priniciple: Our position in the universe is not unqiue. The universe looks the same globally whoever and wherever you are. This forms the basis of big bang theory and implies that the universe is spatially homogeneous and isotropic.
Evidence: 1) Density fluctuations converge to homogeneity beyond 100Mpc as seen by the Hubble telescope. 2) Cosmic microwave background radiation has fluctuation to the order ΔT/^T~10-5. This supports isotropy.
Redshift: Hubble observed that everything in the universe is receding from us. The further away an object, the faster the recession. Empirically the velocity of recession is proportional to distance: v=H0d, where H0=100kms-1Mpc-1h, h is the Hubble constant.
From the redshoft we conclude that in the distant past everything was close together, in an initial explosion or big bang.
Particles: It is crucial to know whether a particle is relativistic or non-relativistic. Baryons are typically non-relativistic while photons and neutrinos are relativistic.
2. Key Equations
2.1 Friedmann Equation
 The equation is expressed in comoving frames, with the expansion r=a(t)x. r is the proper distance and a(t) the scale factor. The constant k=-2U/mx2 is independent of x by homogeneity, therefore the total energy U of a particle must be proportional to x2. k is the curvature of the universe and has a unique value. Note that the Friedmann equation can be derived from both Newtonian and Relativistic mechanics. Λ is the cosmological constant.
2.2 Fluid Equation
To determine the evolution of cosmic density we apply the first law of thermodynamics: TdS=dE+PdV to an expanding unit volume in comoving frame:
 We also need the equation of state P=P(ρ).
2.3 Acceleration equation
Differentiate the Friedmann equation w.r.t time and substitute the fluid equation we get:
 These are all the equation we need to determine the evolution of the universe.
3. Preliminaries
3.1 The Metric Properties:
ds2=guvdxudxv, moving along along a worldline in comoving coordinates, ds2=dt2-gijdxidj. The Friedmann-Robertson-Walker (FRW) line element in spherical polar coordinates is given by:
ds2 = dt2 - a2(t)[dr2/(1-kr2) + r2(dθ2 + sin2θdφ2)]
1) k>0, the universe is closed, like S3.
2) k=0, the universe is flat and Euclidean, like R3.
3) k<0, the universe is open.
3.2 Conformal Time:
t is the proper time (i.e. cosmic time) measured by a comoving observer. Define conformal time by:
dτ = dt/a(t), also dr2/(a-kr2) = dχ2
The metric can be written as:
ds2 = a(t)[dτ2 - dχ2 - f2(χ)(dθ2 + sin2θdφ2)]
1) sinχ k>0
Where f(χ) = 2) χ k=0
3) sinhχ k<0
3.3 The Horizon Problem:
Consider a radial photon, ds2=0 with dθ2=dφ2=0. The proper distance travelled by light since t=0 is given by dH=a(τ)τ. Regions beyong dH have never been in causal contact. The horizon problem states that the microwave sky, despite being isotropic, contains about 105 causally disconnected regions. November 16 The Beauty of Physics [缘起]“ 细推物理需行乐，何为浮名绊此生 ”
—— 杜甫：《曲江二首》
撰写The Beauty of Physics，最初的灵感，来自Random March为我Blog链接所写的说明：科学与艺术的结合。真是知我者，法师也！当年选择物理，一个重要的原因就是觉得这是一门极有美感的学科，这种慑人的美不仅体现在那些简洁，优美的定律和公式中，更深藏在物理学深刻的思辨过程里。无怪乎有人说，哲学是树根，物理学是树干，其他一切学科都是向外延伸的树枝。可惜许多人都因为数学的原因而对物理望而却步，失去了了解这门伟大学科的机会。
那几天整理完一篇西格斯玻色子的小论文，就顺手找了几张高能物理和天体物理的图片（微波背景辐射那张属宇宙学），分三次贴了上来。其实做得很粗糙，选图也不是很认真，没想到大家反响还不错，甚至还激发了同类题材的文章。我于是也有点欲罢不能了，决定慢慢连载下去，不但要包括普通物理的力热光电和相对论、量子论，还要触及一些当代理论物理的分支，比如量子信息论和超弦理论。如果有时间的话，我会写些文字，毕竟物理的逻辑美，是很难用图片来表达的。大家拭目以待吧。
已完成：
November 15 The Beauty of Physics [Part III]令人神往的宇宙是无数艺术家的灵感源泉...
 荷兰印象派画家梵高1889年所作的油画《星夜》
Vincent van Gogh, the Starry Night (1889)
Oil on canvas. The Museum of Modern Art, New York.
 是不是和梵高的画作非常相像？ (© NASA)
 和《星夜》右上角的星云有几分神似吧。位于银河系外侧的麒麟座V838变星（距地球两万光年）
她在2002年初发生爆炸，发出比太阳还亮60万倍的光芒，成为银河系中最亮的恒星。
Variable Star Monocerotis V838 (© NASA)
 最后让我们来看看宇宙中最诡异的物体：黑洞。距地球1万光年的天鹅座超强x-射线源：X-1双星系统。这个公转周期为5.6天的系统包括一个30倍太阳质量的蓝色超巨星（左侧）和一个8-10太阳质量的不可见星体X-1（右侧）。前者的物质不断被吸入X-1，并在X-1周围形成了一个可见的积吸盘。很多科学家认为X-1如果是一颗中子星，其质量应在3倍太阳质量上下，因此它极有可能是一个黑洞。
Cygnus X-1. A powerful X-ray source discovered in 1965. It consists of a blue supergiant star of 30 solar mass and a compact object orbiting around with a period of 5.6 days. The gas flowing from the star towards the its companion forms an accretion disc. The unseen companion, with a mass of 8-10 solar mass, significantly exceeds the upper limit of a neutron star (3 solar mass) and is believed by many as a black hole candidate. November 14 The Beauty of Physics [Part II]“朴至大者无形状，道至妙者无度量。故天之圆也不得规，地之方也不得矩，往古来今谓之宙，四方上下谓之宇，道在其间，而莫知其所。故其见不远者，不可与语大；其智不闳者，不可与论至。”
——《淮南子－齐俗训》
中国古人的宇宙观，竟与当代物理的时空观不谋而和......
In this follow-up we review some breathtaking images from cosmology and astrophysics.
 WMAP卫星描绘出的迄今最清晰的宇宙微波背景辐射地图
Our view of the cosmic microwave background with temperature anisotropies.
This the blueprint of all structures in the Universe. Taken by the WMAP
(Wilkinson Microwave Anisotropy Probe) satellite in 2003.
 我们能观测到的最遥远的星系，距地球超过100亿光年
The most distant galaxy candidates, more than 10 billion light years away!
From the Hubble Ultra Deep Field Probe (© NASA, ESA)
 金牛座内的蟹状星云，距地球6,500光年。这是北宋至和元年（1054年）
中国天文学家记载的一次超新星爆炸的遗骸 (© ESO)
 大型棒旋星系NGC1300， 具有长15万光年的棒状结构。距地球约7,500万光年。
Barred Spiral Galaxy NGC 1300 (© NASA) November 13 The Beauty of Physics [Part I]There are many who regard theoretical physics as dull and uninspiring, lacking any aesthetic value. I am making a humble attempt to show that, on the contrary, it is one of the most beautiful subjects and a towering achievement of human intellect. First let's take a look at some striking images from CERN.
 Simulation of a Higgs decay into four muons in the CMS detector, CERN. (© CERN)
 An artistically enhanced picture of particle tracks in the BEBC. (© CERN)
 Decay of a positive kaon (K+ meson) in flight. (© CERN) November 12 The Mystery of Higgs BosonOne of the most fundamental issues in high energy physics - the origin of mass...
The Search for the Higgs Boson
The Higgs boson is a hypothetical particle to account for the origin of mass. An overview of the Higgs mechanism is presented here, with emphasis on the production of the Higgs boson and searches for the Higgs at LEP. Indication of the production of a Higgs boson at 115GeV has emerged from LEP but further evidence is needed before any conclusion can be made.
The Origin of the Higgs
One of the central questions in today’s research in particles physics focuses on a hypothetical particle called the Higgs boson (H), which if found to exist, may explain the origin of mass. The Higgs boson is closely associated with the electroweak theory, developed and incorporated into the standard model by Abdus Salam and Steven Weinberg in the 1960s. In this theory electromagnetic forces are seen as due to the exchange of photons and the weak forces, which govern radioactivity, are due to the exchange of W and Z particles. Unlike the massless photon, the W and Z are massive particles, weighing 80 and 91 GeV respectively. That is, over 100 time the mass of a proton.
The predictions of the electroweak theory have been verified to very high precision by various experiments. However, there is still one puzzle: the electromagnetic and weak interactions are known to arise from a common symmetry called SU(2)L×SU(1)Y symmetry group and this symmetry indicates that the W and Z particles are massless, just as the photon, which is clearly not true. To solve the puzzle there must be something in addition to the standard model to break the symmetry and give the particles their mass. The simplest solution was introduced by Peter Higgs of Edinburgh University in 1964. Based on the earlier works of Julian Schwinger, Phil Anderson and others, he proposed a new field which permeates all of space and interacts with other particles. The interaction slows the particles down and gives them a mass, the stronger the interaction, the heavier the particles become.
According the wave-particle duality, all quantum fields have a particle associated with them. The particle associated with the Higgs field is called the Higgs boson, corresponding to the disturbance in the field. Further calculation showed that the Higgs boson is spin zero and has neutral charge.
Although the Higgs mechanism itself does not predicts the mass of the Higgs boson, it can be inferred from the precise measurement of the mass of the W, Z and top quark. Combined Data from the Stanford Linear Collider (SLC), the Fermilab and the European Laboratory of Particle Physics (CERN) suggests that the mass of the Higgs boson should be less than 170 GeV, if it is to be consistent with all existing theories.
Search for the Higgs at LEP Physicists have been hunting for the Higgs boson for twenty years, but so far no Higgs were detected. One of the reasons is that the Higgs are very massive. It requires an enormous amount of energy to create it and such an event usually cannot be distinguished from the huge background of other processes. The most thorough search of the Higgs boson so far has been carried out at the Large Electron-Positron (LEP) Collider at CERN. Opened in 1989, the LEP collider is the biggest scientific instrument in the world. The main accelerator (a cyclotron) is built in an underground tunnel 27 kilometres in circumference and consists of four huge detectors: ALEPH, L3, DELPHI and OPAL. Apart from searching for the Higgs boson, particle physicists there also carried out extensive research on the detail properties of the W, Z and top quark. The principle mechanism of producing the Higgs boson at LEP is the so-called the Higgsstrahlung process, i.e. e+ + e- → Z + H.
Both the Z and H are very short-lived and can only be identified by their decay products. The main decay mode for the Higgs is a pair of bottom quark (b) and anti bottom quark (b-), while the Z decays into a quark anti-quark pair (qq-). The main background processes are
e+ + e- → Z + Z and e+ + e- → W+ + W- This was well understood in the early runs of the LEP. The Higgs boson can also be produced in the fusion of W+ and W-, i.e. e+ + e- → W+ + W- and then W+ + W- → H + ve+ + ve- where ve is a electron neutrino and ve- its anti particle. However, this process is quite insignificant in the energy region in which LEP is operated. 2) 2) e+ + e- → (Z → vv-) + (H → bb-). This is the so called missing energy states and occurs with a ratio of 17%. It only has two b jets and the resolution for the Higgs mass is 3 GeV. 3) 3) e+ + e- → (Z → ee-, uu-) + (H → bb-). The ratio is low (6%) but the resolution can be increased to 1.5 GeV since has a low background. 4) 4) e+ + e- → (Z → qq-, ττ) + (H → bb-, ττ). The branching ratio for this process is about 10%. Figure. 1 Computer reconstruction of one of the candidate Higgs events recorded by ALEPH. All four jets are originated from b quarks and anti-quarks. The blue and green jets are believed to have come from the decay of a Higgs boson. (This graph is reproduced from M. Riordan et al., Science 291, 259 (2001))
Final Results from LEP
The LEP was originally designed to have maximum collision energy of 200 GeV and experiments carried out prior to the year 2000 did not reveal any evidence of the production of the Higgs boson. However, in 2000, LEP’s final year of operation, engineers were able to optimize the accelerator and pushed the collision energy up to an unprecedented 206 GeV. Then intriguing results began to appear.
Shortly before the scheduled shutdown, the ALEPH experiment reported on 5 September that they observed a few events which could be interpreted as the production of an 114GeV Higgs boson. This result prompted the CERN board to extend the running of the LEP for another six weeks to the end of November. The final outcome is interesting: Analysis of the data reveals an excess of events consistent with the production of a Higgs boson at 115GeV and incompatible with backgrounds by 3 standard deviation (Figure. 2). That is, the probability that such events are due to the background fluctuation is 4 percent. When the data from DELPHI, L3 and OPAL are added, the significance decreases to 2 standard deviation. With 95% C.L (confidence level), the lower limit of the mass is set to 114GeV. This is not a conclusive result, since a valid claim of a new particle usually requires 5 standard deviation. But it gives us some hint that we are on the right track and there is indeed something out there to be discovered.
Figure. 2 The signals against the mass of the Higgs boson (mh) for (a) NN stream and (b) cut stream. The expectation value of the backgrounds is represented by the dashed line and the shaded areas correspond to 1 and 2 standard deviation respectively. The solid line is the result obtained from the data. Note the large deviation at mh = 115 GeV. (This graph is taken from ALEPH Collaborations, Phys. Lett. B 526 191 (2002)) The Tevatron and the LHC With the closing down of CERN’s LEP collider, the centre of Higgs research shifted to the Tevatron collider at Fermilab. The proton anti-proton (pp-) collider now runs at collision energy up to 1.8 TeV and may produce a Higgs and a W boson in a proton anti-proton collision p+ + p- → W + H, with H decays into a pair of b quark and anti b quark and W → u + v or W → e + v. So far the data samples from Run I are not enough to make a discovery. In March 2001 the newly upgraded Run II began to collect data, but it will take sometime to improve the sensitivity of the devices. By 2006 the Tevatron should be able to see Higgs evidence up to 180 GeV. If nothing is found at the Tevatron, then our best hope lies in the Large Hadron Collider (LHC) at CERN. Now being installed on the site of the original LEP tunnel, the huge proton-proton collider is expected to produce data from 2007. It can reach collision energy of 14TeV and search for the Higgs over a wide range from 100 GeV to 1TeV. The dominant production channel for the Higgs at LHC would be Gluon fusion, i.e. gg → H. At very high energy regions WW and ZZ fusions also become important. Prospects Most theorists are convinced that the Higgs boson will be discovered sometime in this decade at the Tevatron or LHC. However if no Higgs is found, then it would be even more interesting because something must do the job of the Higgs. There are already several alternative theories, one of which is the popular idea of “supersymmetry”. It suggests the existence of several Higgs boson and a new type of strong interaction. In addition, more advanced linear accelerators such as the TeV Energy Superconducting Linear Accelerator (TESLA) in Germany are being designed. They might provide more striking evidence for the Higgs boson. References 1. P. W. Higgs, Phys. Lett. 12, 132 (1964) 2. R. Cahn, Rep. Prog. Phys. 52, 389 (1989) 3. M. Riordan et al., Science 291, 259 (2001) 4. ALEPH Collaboration, Phys. Lett. B 495 1 (2000) 5. ALEPH Collaboration, Phys. Lett. B 526 191 (2002) 6. K. Hagiwara et al., Phys. Rev. D 66, 010001 (2002) 7. J. Glanz, Science 284, 2079 (1999) 8. J. Thompson, LEP’s Glorious Decade, Frontier 9, 19 (2000) 9. B. Murray, Hunting the Higgs, Frontier 14, 19 (2002) 10. S. Schmaltz, Introducing the Little Higgs, Phys. World, November 2002 11. G. Collins, Higgs Won’t Fly, Scientific American, February 2001 12. S. Tomlin, Nature 409, 754 (2001) July 13 Finally, our paper is published!After a year-long preparation, a revised version of our paper is finally published in New Journal of Physics. I'm glad that I have produced "publishable" results from the project.
I. Carneiro, M. Loo, X. Xu, M. Girerd, V. Kendon, P. Knight, Entanglement in coined quantum walks on regular graphs, 2005 New J. Phys. 7 156
The paper is available online at: http://stacks.iop.org/1367-2630/7/156 |
）。以大爆炸为起点在同移参照系里测得的时间一般称作宇宙学时间，按照这个标准，从宇宙诞生到现在已经超过130亿年了。在考虑非同移的天体时，要通过时空变换来计算相对于该天体静止的坐标系里的时间。严格地说，主要天体（包括地球）都不是理想的同移参照系，但是通常它们相对于同移参照系的运行速度都很小，可以忽略不计。|
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