I just want to be a quiet scholar

Chapter 336 Complexity

The Princeton Institute for Advanced Study was as calm as ever.

Shen Qi came to visit his physics tutor Witten, and talked about his ideas: "Navier and Stokes actually use calculus to explain fluid motion. Although the Navier-Stokes equation has not yet found a mathematical But Neville's name is engraved on the Eiffel Tower, and Stokes is Professor Lucas of Cambridge."

Witten said: "Comparatively speaking, Stokes' mathematical ability is stronger. Most of the mathematical processing in the NS equation comes from Stokes. He has gained a greater commemoration. There are craters named after Stokes."

"I am good at differentiation, integration and partial differentiation, but I am a layman about fluid motion. Recently, I am studying fluid motion." Shen Qi reported his recent progress in physics.

Witten asked: "So you want to find the mathematical solution to the NS equation?"

"It's difficult, but I try my best. It takes a lot of time and a little bit of inspiration. So Edward, let's talk about the Yang-Mills equation. Compared with the NS equation, the Yang-Mills equation involves The field is much more complex."

"Classical mechanics, quantum mechanics, quantum field theory, energy chain waves and cosmology, and your string theory, just a QFT gives me a headache. GUT seems to be a legend." Shen Qixian's distress, QTF is quantum field theory The abbreviation of GUT is the grand unified theory that all physicists dream of.

"So you want to solve the NS equation and the Yang-Mills equation at the same time?" Edward Witten expressed surprise.

Shen Qi shook his head and said, "This is too difficult, I want to hear your opinion."

Witten: "I can't give any opinions for the time being. Let's talk about it after you get a Ph.D. in physics."

"Oh, by the way, Edward, I came with questions. We all know that condensed matter physics is more like a bridge. It connects quantum mechanics and classical physics. We can find Yang-Mills equations in condensed matter physics. The research report can also find marginal intersections of NS equations, so what do you think about the complexity mentioned in condensed matter physics?" Shen Qi asked.

The concept of complexity was actually first proposed by PW Anderson, and Witten elaborated in his own language: "In the physics world, complexity is still an unresolved issue, from the image of the spin lattice to the well-known The Turing machine, from the second law of thermodynamics to the devil's ladder, from the rice pile experiment to chaos theory, from turbulence to earthquakes, seemingly unrelated things are connected and follow a certain law, this is complexity."

"However, most of the current complexity laws mainly rely on the intuition of physicists, such as PW Anderson, and we lack the necessary quantitative explanation. Hey, boy, let me ask you, from the graphite phase nitrogen carbide you study every day, According to the principle of complexity, what can you think of?" Wei Teng took advantage of the topic and chatted very happily.

Shen Qi immediately replied: "Friction."

Wei Teng was curious: "Friction? Very novel answer, can you tell me about your friction?"

Shen Qi rubbed his hands: "There are defects in matter. I use the topological method based on homotopy groups to define material defects. According to my paper published on PRL, Professor Hackman uses physical and chemical methods such as doping and tailoring to improve, Reorganize the molecular structure of graphitic nitrogen carbide, which is friction in the microscopic scale."

Shen Qi kept rubbing his hands together, rubbing faster and faster until his palms became hot: "Friction, friction, the steps of the devil, multiply the carbon atoms in the graphite-phase nitrogen carbide by about 10 to the 17th power, and it becomes the earth Friction friction, can the defects of the earth be optimized through friction? This is the complexity I can think of, unfortunately, I can’t give quantitative support, it’s just an intuition without evidence.”

"Then find the certificate." Witten ended today's conversation.

Shen Qi rubbed his hands all the way back to his office, unable to stop at all.

The complexity theory in condensed matter physics is a very mysterious thing, if you don't study it, it's enough. Once you study it deeply, Shen Qi becomes obsessed.

"Scrub, rub."

Shen Qi rubbed against each other for a whole afternoon, repeating these two words over and over again.

Seemingly without purpose, Shen Qi casually clicked on the ADF software in the computer and found the simulated molecular structure diagram of the GaN crystal. It was like a piece of wallpaper, strictly obeying the symmetrical arrangement rules. The white balls represent gallium atoms, and the black balls represent gallium atoms. Nitrogen atoms, criss-crossed, extend infinitely.

Shen Qi operated the mouse, and the mouse rubbed against the mouse pad.

Performing TDDFT calculation on GaN quantum dots can obtain the ultraviolet-visible absorption spectrum of GaN quantum dots.

光谱曲线非常明显，GaN在300-1500nm之间有五个不同吸收强度的吸收峰，其中心位于401nm处的最强吸收峰主要来自HOMO-11→LUMO（95%）的电子跃迁。

"Friction rubs, expands and collapses."

Shen Qi cut back the schematic diagram of the planar molecular structure of GaN crystal, and the simulation experiment calculation results verified the mixed dislocations in GaN.

The dislocation slip moves along the plane formed by the dislocation line and the Burgers vector, and the dislocation climb is realized by the expansion or contraction of the semi-atomic plane at the edge of the dislocation.

Diverging along this line of thought, Shen Qi instinctively made a mathematical calculation based on the dynamics of the two-dimensional lattice OFC model in the case of 0≤α≤1/4.

The calculations are based on the steady Navier-Stokes equations with Dirichlet boundary conditions.

At present, it can only be assumed that the NS equation is established. For hundreds of years, scientists have assumed the NS equation to be established, obtained a large number of theoretical research results, and applied them to practice.

If the NS equation is not established, how can the plane soar in the sky?

The NS equation is always performed in nature, but people cannot find its mathematical solution.

Shen Qi's thinking has been jumping, from gallium nitride, the core material of blue light-emitting diodes in semiconductor lighting, to the NS equation.

Two seemingly unrelated existences, interspersed with the complexity principle of condensed matter physics, friction, friction.

Because there is no connection, the amount of calculation is extremely huge.

Shen Qi calculated until late at night, forgot to eat, and forgot to go home.

Ouye, who was alone in the empty boudoir, called: "What time do you go home?"

"Oh, go home, it's 12 o'clock." Shen Qi returned to the staff dormitory with a pile of draft paper in his arms.

"Are you busy?" Ouye heated up the chicken soup that had been cooked at 7 o'clock, and put it on the dining table.

"I'll drink the soup first, and you can calculate a set of data for me. You don't need to know the cause and effect. It's OK to solve this equation through the low-order finite element method." Shen Qi gave Ouye a calculation task, and he drank I ordered chicken soup, which tastes good, but there is too much salt.

"This is... the Dirichlet boundary condition, the NS equation?" Ouye had studied mathematical physics methods when he was an undergraduate. It looks so beautiful.

"Have you forgotten all the mathematical and physical methods?" Shen Qi asked with a smile.

"Underestimate me?" Ouye rolled Shen Qi's eyes, and the heart of the calculation girl in girlhood was burning.

In just a bowl of chicken soup, Ouye made the most efficient calculations through purely mathematical calculations without knowing the ins and outs.

"It's amazing my Ye, cut NS with warm soup." Shen Qi double-checked the calculation results.

This calculation result made Shen Qi and Ou Yejun somewhat puzzled.

υ1（x1，x2）=（x1δ（i+j）+x2γ（i-j-1））（x1δ（i+j+1）^2+x2γ（i+j-1）^2）……

υ2（x1，x2）=（x1δ（i+k）+x2γ（i-k+1））（x1δ（i+k-1）^2+x2γ（i-k+1）^2）……

……

"I don't know what this group of calculation results represent, what is their specific meaning? Just from the principle of mathematical calculation, they are correct results." Shen Qi can only explain this, and he shook his head: "I went to Weibo this morning. Go there, get some enlightenment, and then think hard all day, what crystal defects, dynamics, NS equations, thinking jumps to fly, self-indulgent, and come to such a meaningless mathematical result."

"Not every mathematical calculation result has practical significance." Ouye said.

"Hehe, your consciousness is getting higher, Little Ye Zi." Shen Qi turned on the TV, ready to watch TV for a while and sleep.

CNN is broadcasting a news message: "An earthquake with a magnitude of 6.5 occurred on the Pacific Ocean southwest of San Diego yesterday. The tsunami triggered by the earthquake hit San Diego. Fortunately, no casualties were caused."

Shen Qi jumped up in a jerk, rubbing, rubbing!
Earthquakes are frictions within the earth.

The TV screen showed that the epicenter was located on the bottom of the Pacific Ocean, with the coordinates being 32 degrees 30 minutes north latitude and 117 degrees 19 minutes west longitude.

(End of this chapter)