Personal Statement V7.3
Zhixin Lu
I love sciences since I was young. I owned a laboratory of physics and chemistry when I was 9
built with my twin brother in the balcony of our house. I have observed the amazing supercooled
liquid (-18 centigrade) at 13 when I was examining the Mpemba effect which I’ve seen from a
magazine asserted that hot water might freeze faster than warm water. When 16, I accidentally
witnessed and studied the long time existence of droplets floating on the surface of the same liquid
when drinking Coca Cola and realized that it was a good example of metastability in
thermodynamics. When noticed that bubbles in ice layer are not well-distributed on lake, I finally
found that the condensation of purples is a cosine function of the angle of inclination under water
and designed an experiment to attest it.
During college, I did not only learn those courses but also made great effort to solve problems I
faced by off-the-wall ideas I’d came up with. By imagining the Brachistochrone curve as a beam
of light going through an inhomogeneous media whose refractive index is a function of altitude
that makes the light seems accelerated by gravity, I simplified the calculation of the
Brachistochrone curve by a simple integration rather than using the calculus of variations. After
that, I realized that physical insight will help simplifying many problems. I proposed a new
algorithm based on the Huygens-Fresnel principle and the time reversal method to solve the
Optimal Path problem in a complex time-varying environment, and achieved the second order
prize of the Challenge Cup in 2009. I used to periodically reviewing articles and scientific news
from website like science daily and some scientific journals. The discovery that magnetic
monopole exists at the end of the Dirac String (D.J.P. Morris et al., 2009) reported in Science led
me to consider: Is the property of magnetic charge the same with electronic charge? I reckoned
that the magnetic charge is not invariant like the electronic charge under the Lorenz
transformation considering that the magnetic field density is a 3-order inverse symmetric tensor
but electronic field density is a 3-dimensional vector and have done some calculation on it.
All those experiences make my desire of doing some real theoretical research stronger and
stronger and I decided to choose the Einstein-Pauli-Yukawa Paradox (Guangjiong Ni, Acta
Photonica Sinica 28, 112 (1999).) which is an open question in Quantum Mechanics as my
graduation thesis. To explain why Einstein’s calculation indicates that the momentum spectrum of
a particle lying in 1-dimensional infinite well is discrete, I carefully compared his method with the
widely used Landau’s approach based on the superposition principle of state. The essential
divergence of them I found is actually the definition of the eigenfunction of momentum where
Einstein, Pauli, Yukawa believed that the eigenfunction of momentum in this situation should be
zero out side the infinite well. I proposed that the momentum spectrum obtained by Landau’s
approach can be seen as a measuring result of suddenly open the potential well whereas Einstein’s
shows the momentum before taking any measurement.
从 EPY 的科研我发现，偶然遇到的小 topic 固然有趣，但是要想做系统的东西还是要大量阅
读文献和教材。
Though small topics I have done are interesting, it made me feel like a child losing the way home
as those topics seemed unrelated between each other. The procedure of proposing and self-denying
again and again before I got my final conclusion about the EPY paradox made me realize that
research should not only involved in one’s innovations but also provide a chance to promote one’s
ability. Also, I find theoretical research more appealing to me and, in my opinion, clean and pure.
过去的科研给我的感觉就是我一个没有家的孩子，这做一个那做一个，碰到什么做什么。从
EPY 开始，我很希望能做一个能够不断深入，可以引出新的问题或者完善没有完善的理论
体系的科研，这会让我更加有成就感并且选择一个喜欢的方向是非常必要的。
Different from those small topics I have done before, I did not only rely on innovations and ideas
of myself but also read lots of papers about EPY Paradox and try to form my own opinion about it.
During this, I had proposed several explanations and self-denied them after widely read and
deliberation. Since then I wish to do more researches in a standard way and finally I went to
Tsinghua University.
In the last semester, I became enchanted with nonlinear dynamics after reading the Chance and
Chaos (David Ruelle, 1993) and self-learned the Nonlinear Dynamics and Chaos (Steven H.
Strogatz, 1994). After graduation, I got involved in Professor Lan’s nonlinear dynamics group to
do researches on theoretical nonlinear physics. I am now reading books Chaos: Classical and
Quantum (Predrag Cvitanovic et al., 2009) and Chaos in Dynamical Systems (Edward Ott, 2002).
Current Research:
Recently, the collapse transition of a two dimensional meta-flexible polymer is proved to be
first order (Haijun Zhou et al., 2008) by analytically calculating the free-energy density
when N goes to infinite in lattice model. Considering that the thermodynamics limit will
increase the height of the barrier between two phases and vanish the transition rate between
metastable states (Weimou Zheng, 2006), I improved the calculation and derived the
partition function and free energy density for polymer with limited N which showed the
coexistence of metastable states, and derived the possibility for polymer to transit between
globule and coil phase in time t by the Fokker-Planck Equation. A MC simulation was also
implemented for verifying the theoretical prediction. Being feasible to confine polymers to
2D mobile surfaces (B. Maier et al., 1999), it is possible to verify the theoretical prediction
experimentally. The theoretical result is also applicable to the problem of protein β-sheet
unfolding.
新的科研，
Nonlinear Dynamics is now applied in many fields of Physics and playing an important
研究兴趣
Why Nonlinear Science:
I had seen the movie ‘A Beautiful Mind’ before and was impressed by Nash and his brilliant work.
I take thinking about science and the world at liberty as a great honor. That is why I keep
self-learning and studying much though it is not that easy (most guys majored in physics leave this
field in many reasons, what a shame.). At the end of that movie, Nash said that he had asked
himself what decide the reasons. His answer is love but I think it lies in nonlinear science because
of the fact which astonished me when I realized at first time that even the most simple equations
can evaluate into a colorful world. God who made this world lies everywhere because of the
world’s nonlinearity. I believe that some big answer of this amazing world will be found here.
Though I am not a talent like Nash and many other famous scientists at present, I believe that one
day, I will come to some hidden principles or rules and show them to the world if I keep thinking
and working hard like Nash.