Writings

For my solutions to the assignments of the course Introduction to Cold Atoms, please click here. Lecture notes || The serial lectures were titled Quantum Many-Body Correlation Functions and Applications to BEC. My notes covered the first half of the lectures, namely, static/dynamic structure factors in X-ray/neutron scattering and linear response theory with special emphasis on causal commutators. I included a complete derivation of f-sum rule which is really nontrivial! More on Hui Zhai's page. ||
 * Notes of Alexander Fetter's lectures at Tsinghua || Spring, 2012 ||
 * [[file:ALFetterChina2012-2.2.pdf]]


 * Manifolds of Classical Mechanics || Summer, 2010 ||
 * [[file:ClassicalMech.pdf]]

Essay || Below is the abstract. Some people claim that Lagrangian Mechanics is not “geometrical,” I disagree. In the mean time, many physicists quote “conﬁguration space” without a detailed geometrical description. Refutation to that point and establishment of the geometrical picture will be presented in this article. Certainly, I will not conﬁne the focus on Lagrangian mechanics only, nevertheless, I will portrait the big picture of classical mechanics. And diﬀerential geometry is the language used in the drama where three important manifolds will be our leading roles. They are named as Euclid-Newtonian manifold, conﬁguration space (Lagrangian manifold) and phase space (Hamiltonian manifold) respectively. Finally, we will have a uniﬁed landscape for classical mechanics. ||


 * The Language of General Relativity || Summer, 2010 ||
 * [[file:notes_on_GR.pdf]]

Notes || A short summary of important equations and formulas. There are two reasons why general relativity is diﬃcult. One is that the geometrical picture is hard to visualize: 4 dimensional, curved spacetime. The other one is the startling tensor algebra. Frankly speaking, nobody could visualize 4-D curved space without the help of logic and analogies which indeed take a lot of talents. Nevertheless, once you conquered the algebra, the pain would be much eased. This article is a summary of my knowledge of the algebra ||

Solutions || <span style="font-family: Georgia,serif;">My solutions to the problems of the book Atomic Physics written by Christopher J. Foot. It was done to exchange homework credits of freshman physics Quantum Physics under the approval of professor Mei Zhang. ||
 * <span style="font-family: Georgia,serif;">My solutions to problems of Atomic Physics (Foot) || <span style="font-family: Georgia,serif;">Summer, 2011 ||
 * <span style="font-family: Georgia,serif;">[[file:FootAtomicSoln.pdf]]


 * <span style="font-family: Georgia,serif;">Universe in a Grain of Salt || <span style="font-family: Georgia,serif;">Summer, 2011 ||
 * <span style="font-family: Georgia,serif;">[[file:particle.pdf]]

<span style="font-family: Georgia,serif;">Essay || <span style="font-family: Georgia,serif;">My final essay for the course Introduction to Particle Physics, the abstract of which is as follows. Our universe behaves like a crystal and the matters are just excitations from the ground state. In this paper, we learn that special relativity is nothing special, it is equivalent to an elastic theory of lattice waves and dislocations. In the long wavelength limit, the ether is completely invisible and what we see are excitation modes of ether. Since we cannot see the ether though it may exist, then there is still no preferred frame of reference and hence it does not contradict the Lorentz invariance. However, when the energy scale is around the Planck scale, it is possible for the background material, ether, to show up and provides an absolute frame of reference and hence breaks Lorentz invariance. Theory of string-net condensation consolidates the picture of ether. Gauge bosons and fermions are shown to be the results of the motions of the invisible string-nets on a cubic lattice. ||


 * <span style="font-family: Georgia,serif;">"Hard" Issues in Softmatter Physics || <span style="font-family: Georgia,serif;">Summer, 2011 ||
 * <span style="font-family: Georgia,serif;">[[file:HardIssuesinSoftmatter.pdf]]

<span style="font-family: Georgia,serif;">Essay || <span style="font-family: Georgia,serif;">The final essay for the course Introduction to Softmatter Physics (Dadong Yan). This article serves as a survey of polymer ﬁeld theory, from the background to its formalism. Concept of Gaussian chains, Brownian motion picture and n-point transition probability are clariﬁed which serve as the foundation of a polymer ﬁeld. Then the polymer ﬁelds and path integral formalism are introduced, making reference to similar aspects of quantum mechanics. Based on the formalism, mean ﬁeld theory and Gaussian ﬂuctuation are discussed in detailed and renormalization group theory is also mentioned. The mean ﬁeld is interpreted as the ground state of a polymer ﬁeld with Gaussian ﬂuctuations as elementary excitations and correlations energies found in strong ﬂuctuation systems through Hartree approximation are identiﬁed as scattering interactions between the quasiparticle ‘polymerons.’ ||


 * <span style="font-family: Georgia,serif;">Field-theoretic interpretations of Ginzburg-Landau theory of superconductivity || <span style="font-family: Georgia,serif;">Winter, 2012 ||
 * <span style="font-family: Georgia,serif;">[[file:superconductivity.pdf]]

<span style="font-family: Georgia,serif;">Essay || <span style="font-family: Georgia,serif;">The final essay for the course Introduction to Superconductivity (Jiacai Nie). Ginzburg-Landau theory of superconductivity is derived from microscopic BCS theory in terms of path integral formalism. Expression for the supercurrent is obtained from the Ginzburg-Landau action which is exactly the equation of motion of the massive photon ﬁeld. It is further pointed out that the London penetration depth is actually the Compton wavelength of the massive photon. ||


 * <span style="font-family: Georgia,serif;">Extended form of second law of thermodynamics || <span style="font-family: Georgia,serif;">Spring, 2011 ||
 * <span style="font-family: Georgia,serif;">[[file:Extended_form_of_2nd_law.pdf]]

<span style="font-family: Georgia,serif;">Lecture slides || <span style="font-family: Georgia,serif;">A short presentation on a letter titled extended form of second law of thermodynamics, during the course Introduction to Biological Physics (Zhanchun Tu). Instead of going through all the formidable equations in the letter directly and leaving the audience asleep, I first introduced some basic concepts such as the master equations, and in order to provide a intuitive picture for the audience, I interpreted the probability distribution as electric charge density. Next I explained the difference between a steady state and detailed balance by demonstrating a simple example illustrated with graphs. Then I came to the details of the letter and pointed out and corrected an error in it. ||


 * <span style="font-family: Georgia,serif;">Demonstrations of image transformation with a liquid crystal light valve || <span style="font-family: Georgia,serif;">Summer, 2012 ||
 * <span style="font-family: Georgia,serif;">[[file:report_lclv.pdf]]

<span style="font-family: Georgia,serif;">Lab Report || <span style="font-family: Georgia,serif;">This experiment is a laboratory implementation of Fourier optics which I think is one of the sweetest marriage between mathematics and physics. The abstract formalism of Fourier transform found an extremely simple physical incarnation, a lens!

<span style="font-family: Georgia,serif;">In this lab report, the experimental setup was drawn with Inkscape while the data were analyzed and plotted using gnuplot. ||


 * <span style="font-family: Georgia,serif;">Weak signal processing with lock-in amplifier || <span style="font-family: Georgia,serif;">Spring, 2012 ||
 * [[file:report_lockin.pdf]]

<span style="font-family: Georgia,serif;">Lab Report || <span style="font-family: Georgia,serif;">This experiment impressed the most due to its power in application and mathematical beauty. Lock-in amplifiers are widely used in the measurement of extremely small signals with known frequencies mixed among strong noise. The mathematics behind is Fourier transform and filtering in frequency space which is just elegant. ||


 * <span style="font-family: Georgia,serif;">Perspective analyses of two reports on Chen Guangcheng's arrest and trials || <span style="font-family: Georgia,serif;"> Summer, 2012 ||
 * <span style="font-family: Georgia,serif;">[[file:ChenGC.pdf]]

<span style="font-family: Georgia,serif;">Essay (Humanity) || <span style="font-family: Georgia,serif;">The only non-science essay listed on this page. In this essay, I analyzed two news reports on Chen's arrest and trials, in terms of the stands, aspects of interest and purposes of writing. ||