The Institute for Advanced Study in Princeton is as calm as ever.

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

"Stokes is more mathematically capable than to mention, and most of the mathematical processing in the N-S equation comes from Stokes, and he has received a greater kind of memorial, as there are craters named after Stokes on both the Moon and Mars," Witten said. ”

"Differentiation, integration, partial differentiation, I'm good at that, but I'm a layman when it comes to fluid motion, and lately I've been studying fluid motion. Shen Qi reported on his recent progress in physics.

Witten asked, "So you want to find the mathematical solution to the N-S 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, which is much more complex than the N-S equation. "Classical mechanics, quantum mechanics, quantum field theory, energy chain waves and cosmology, as well as your string theory, just one QFT gives me a headache, and GUT seems like a legend. Shen Qixian's distress, QTF is the abbreviation of quantum field theory, and GUT is the grand unified theory that all physicists dream of.

"So you want to solve both the N-S equation and the Yang-Mills equation at the same time?" said Edward Witten.

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

Witten: "I can't give you any opinions for the time being, so let's wait until you get your Ph.D. in physics." ”

"Oh, by the way, Edward, I'm here with a question, we all know that condensed matter physics is more like a bridge, it connects quantum mechanics and classical physics, we can find research reports related to the Yang-Mills equation in condensed matter physics, and we can also find marginal intersections of the N-S equation, so what do you think about the complexity mentioned in condensed matter physics?" Shen Qi asked.

Anderson was the first to put it up, and Witten elaborated it in his own words: "In physics, complexity is still an unsettled problem, from the image of a spin lattice to the well-known 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 linked together and follow some kind of law, and that is complexity." ”

"However, most of the laws of complexity at present rely primarily on the intuition of physicists, and Anderson, we lack the necessary quantitative explanations. Hey, kid, then let me ask you, what can you associate with the graphitic nitrogen carbide that you study every day, according to the complexity principle?"

Shen Qi immediately replied: "Friction." ”

Witten was curious: "Friction? Very novel answer, can you tell us more about your friction?"

Shen Qi rubbed his hands: "There are defects in matter, I use topology based on homotopy groups to define material defects, Professor Hackman according to my paper published in PRL, use doping, tailoring and other physical and chemical means to improve and reorganize the molecular structure of graphite nitrogen carbide, which is friction in the microscopic. ”

Shen Qi kept rubbing his hands, rubbing faster and faster, rubbing until his palms were hot: "Friction and friction, the devil's pace, put the carbon atoms in the graphite phase nitrogen carbide about 10 times to the 17th power, and it will become the size of the earth." Friction, can the defects of the earth be optimized by friction? That's the complexity I can relate to, and unfortunately, I can't give a quantitative support, just an unsubstantiated intuition. ”

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

Shen Qi rubbed his hands all the way back to his office, and couldn't stop at all.

The complexity theory in condensed matter physics is a very mysterious thing, and if you don't study it, you can only do it, and once you study it deeply, Shen Qi will become obsessed.

"Rub, rub. ”

Shen Qi rubbed for a whole afternoon, repeating these two words.

Seemingly without any purpose, Shen Qi casually clicked on the ADF software in the computer and found the simulated molecular structure diagram of the GaN crystal, which is like a wallpaper, strictly abiding by the rules of symmetry arrangement, the white ball represents the calcium atom, the black ball represents the nitrogen atom, crisscrossing and extending infinitely.

Shen Qi operates the mouse, and the mouse rubs on the mouse pad.

The ultraviolet-visible absorption spectrum of GaN quantum dots can be obtained by TDDFT calculation of GaN quantum dots.

The spectral curve is very obvious, GaN has five absorption peaks with different absorption intensities between 300-1500 nm, and the strongest absorption peak at 401 nm is mainly from the electronic transition of HOMO-11→LUMO (95%).

"Friction friction, expansion and collapse. ”

Shen Qi switches back to the schematic diagram of the planar molecular structure of the GaN crystal, and the simulation experimental results verify the mixed dislocations in GaN.

The slip of the dislocation moves along the plane formed by the dislocation line and the Burgess vector, and the dislocation is achieved by the expansion or contraction of the semiatomic plane at the edge of the dislocation.

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

The calculation is based on the stationary Navier-Stokes equation with Dirichlet boundary conditions.

At present, it can only be assumed that the N-S equation is true, and for hundreds of years, scientists have assumed that the N-S equation is true, and a large number of theoretical research results have been obtained, and they have been applied to practice.

If the N-S equation is not true, then how can an airplane soar into the sky?

The N-S equation is always deduced 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 N-S equation.

Two seemingly unrelated beings, interspersed with the principle of physical complexity of condensed matter, friction, friction.

Because it is unrelated, it is extremely computationally intensive.

Shen Qi calculated until late at night, forgetting to eat and going home.

Ou Ye, who was alone in the empty boudoir, called: "What time will you go home?"

"Oh, go home, it's 12 o'clock. Shen Qi held a pile of scratch paper and returned to the faculty dormitory.

"Busy?" Ou Ye heated up the chicken soup that had been cooked at 7 o'clock and put it on the table.

"I'll drink the soup first, you help me calculate a set of data, you don't need to know the cause and effect, through the low-order finite element method, it's OK to solve this equation." Shen Qi gave Ou Ye a calculation task, and he drank the chicken soup, which tasted good, but there was too much salt.

"It's ...... Dirichlet boundary conditions, N-S equations?" Ou Ye studied mathematical physics methods when he was an undergraduate, and scored 99 points in the exam, and he didn't give one point because the female teacher of mathematical physics methods said that Ou Ye was too beautiful.

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

"Look down on me?" Ou Ye glanced at Shen Qi, and the heart of the girl's generation was burning.

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

"Awesome my leaves, warm soup chop N-S. Shen Qi double-checked the calculation results.

This calculation result made Shen Qi and Ou Ye a little confused.

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 these calculations represent, what they mean, but they are correct in terms of mathematical principles. Shen Qi could only explain like this, he shook his head: "I went to Witten this morning, got some enlightenment, and then meditated all day, what crystal defects, dynamics, N-S equations, thinking jumped to flying, and I was so excited that I couldn't get such a meaningless mathematical result." ”

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

"Yo, the consciousness is getting higher, little leaf. Shen Qi turned on the TV and prepared to watch TV for a while and go to sleep.

CNN is broadcasting a news message: "Yesterday, an earthquake measuring 6.0 on the Richter scale struck the Pacific Ocean southwest of San Diego, and the tsunami caused by the earthquake hit San Diego, but fortunately there were no casualties. ”

Shen Qi jumped up with a spirit, rubbing, rubbing!

An earthquake is a friction in the interior of the earth.

Television footage shows that the epicenter is located on the bottom of the Pacific Ocean, and the coordinates are 32 degrees 30 minutes north latitude and 117 degrees 19 minutes west longitude.