ChenchaoZhao
For my solutions to the assignments of the course Introduction to Cold Atoms, please click here.
Notes of Alexander Fetter's lectures at Tsinghua
Spring, 2012

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.

Manifolds of Classical Mechanics
Summer, 2010


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


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

My solutions to problems of Atomic Physics (Foot)
Summer, 2011

Solutions
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.

Universe in a Grain of Salt
Summer, 2011


Essay
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.

"Hard" Issues in Softmatter Physics
Summer, 2011


Essay
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.’

Field-theoretic interpretations of Ginzburg-Landau theory of superconductivity
Winter, 2012


Essay
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.

Extended form of second law of thermodynamics
Spring, 2011


Lecture slides
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.

Demonstrations of image transformation with a liquid crystal light valve
Summer, 2012


Lab Report
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!

In this lab report, the experimental setup was drawn with Inkscape while the data were analyzed and plotted using gnuplot.

Weak signal processing with lock-in amplifier
Spring, 2012


Lab Report
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.

Perspective analyses of two reports on Chen Guangcheng's arrest and trials
Summer, 2012


Essay (Humanity)
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.