Chapter 474 The Answer to the Strongly Correlated Electron System!

Xu Chuan was stunned at the reporting table.

The narrating voice stopped, and the audience in the audience was also stunned for a moment.

What's going on here?

Isn't the report completed? Why are you so stunned on stage?

What's going on? Or what?

Although most of the mathematicians here have not understood the report on strongly correlated electron systems, there are still many mathematicians here who are interested in mathematical physics.

During Xu Chuan's lecture, most people consulted their colleagues and learned about the importance of the problem of strongly correlated electronic systems to physics.

This is a problem that is no less important than the seven millennium problems in mathematics. If it can be solved, it will greatly promote the development of materials science, condensed matter physics, quantum physics and other fields.

Although it is unclear why this top expert would report such a thing at a mathematics seminar, people are generally quite tolerant of experts.

So even though Xu Chuan was standing on the reporting table in a daze, no one made a sound to disturb him. They just discussed and communicated with each other in a low voice under the stage.

In the front row of the lecture hall, Terence Tao was quietly communicating with Peter Schultz who was sitting next to him.

He didn't pay much attention to it at first, but looking at the figure standing on the stage, an electric arc suddenly flashed in his mind, and the expression on his face suddenly became solemn.

On the side, Schultz looked at Terence Tao who was sitting upright for no reason, and asked curiously: "What's wrong?"

Tao Zhexuan took a deep breath and said: "I remembered the video of him proving the NS equation before. At that time, he also stood in meditation for a long time in class, and then solved the NS equation in one fell swoop."

"And the proofs and tools of that time are as if they were written by God to the mathematical world."

"perhaps."

"Today we get to see another miracle."

Hearing this, Schultz also remembered the video about the NS equation, smiled, and said, "Tao, maybe you are thinking too much."

Laughs "It's just that kind of miracle and inspiration. You're lucky to do it once in your life. If you can do it every time, it's incredible."

After a pause, he then joked: "In that case, I would doubt whether he is the reincarnation of God."

Tao Zhexuan shook his head and said, "Look, I think my feeling is not wrong."

At the reporting table, Xu Chuan ignored it, or at this moment he didn't even think that he was still on the stage.

He stood there motionless, completely forgetting his surroundings and the hundreds of listeners in front of him.

In his mind, the door that locked the problem of strongly correlated electronic systems clearly appeared.

And the key to open that lock is constantly being tempered and shaped.

The exchange with Witten made him think of another way to break through this abyss.

That is dimensional space!

To be precise, it should be the dimension, and the impact of dimension on the properties of strongly correlated electronic systems.

In materials science, dimension is a real concept that is similar to, but different from, dimensions in physics.

For example, low-dimensional materials refer to materials that do not exceed the nanometer level in three dimensions, specifically two-dimensional, one-dimensional and zero-dimensional materials.

Zero-dimensional materials are also called quantum dots. They are composed of a small number of atoms or molecules, and the size of the particles is on the nanometer scale. Atom clusters of semiconductors and metals are typical zero-dimensional materials.

One-dimensional materials are called quantum wires, and the thickness of the wires is on the order of nanometers. For example, carbon nanotubes and one-dimensional graphene are one-dimensional materials.

Two-dimensional materials include an interface between two materials, or a thin film attached to a substrate. The depth of the interface or the thickness of the film layer is on the nanometer scale, such as metal nanoplates.

In the early years, he participated in the tungsten diselenide material project of NTU mentor Chen Zhengping.

Tungsten diselenide is a typical two-dimensional material.

In low-dimensional materials, the impact of dimensions on the material itself is an option that cannot be ignored.

Especially in materials such as complex transition metal oxides (TMOs), due to strong electron-phonon or electron-electron coupling, the collective behavior of system electrons determines its macroscopic properties.

The simple superposition of the kinetic energy of a single electron no longer plays a dominant role. It will change with changes in external conditions such as temperature and magnetic field, as well as various order parameter phases such as the lattice structure, electronic structure and spin arrangement of the material.

They are entangled with each other, resulting in extremely rich phase diagram structures.

It then displays macroscopic quantum phenomena such as high-temperature superconductivity and giant magnetoresistance, giving the material new properties with great application value.

In this process, the impact of dimensions on it is a question that Xu Chuan is thinking about.

By regulating the coupling strength between multiple degrees of freedom by changing the quantum confinement effect generated by the dimensions of a strongly correlated system, we can controllably induce richer physical phenomena. This is a truth that can be proven through experiments.

What he is thinking about now is how to explain it using mathematics.

Perhaps by achieving this, a more universal unified theoretical framework can be found to unify the strongly correlated electronic system.

In this way, he stood on the stage and began to think logically, forgetting the environment he was in.

In the lecture hall, the mathematicians in the audience were also waiting patiently.

Time passed little by little in this quietness.

One minute.

Two minutes.

five minutes.

In the blink of an eye, ten minutes passed.

The crowd below the stage was more agitated than before, but everyone was still trying to keep a quiet atmosphere. Since they were talking, they kept their voices down so as not to interfere with the thinking on the stage.

At this point, the scholars in the lecture hall probably knew that this young expert seemed to have a new inspiration.

Although the strongly correlated electron system is not a difficult problem in the mathematical world, everyone present is looking forward to some new breakthroughs in it.

After all, mathematics is the foundation of all natural sciences and the language of other disciplines.

If physics is a discipline that studies natural laws and logic, then mathematics itself is logic.

It is a thinking tool created by human beings subjectively, and it is a logic that is further simplified based on existing natural laws and logic.

The things that humans can touch within this cosmic constant are so limited, but mathematics has given infinite possibilities and brought infinite beauty to humans.

It belongs to Venus born in foam, and also to the aria on the G string. You can experience the vicissitudes of the coastline from natural fractals, or create a grand starry sky in a conservative chaotic system, and even create your own artificial intelligence in vector space.

In the lecture hall, several students who followed their mentors to attend the seminar for the first time clenched their fists involuntarily, feeling a little worried and at a loss.

Although they were not standing on the podium in person, they seemed to be able to empathize with the tension.

Of course, what they didn't know was that their mentors standing on the stage were not nervous at all.

Time passed by little by little, and no one knew how long it had passed. Just when the staff under the stage were hesitating whether to report to the leader and remind him that the third report meeting should start, Xu Chuan, who had been motionless, suddenly moved.

He turned around and took down the eraser from the hook of the mobile blackboard, and wiped the previous calculations on the blackboard clean in a few strokes.

Then, a white chalk point fell on the black panel, and lines of formulas quietly jumped with the dance of the palm.

【χ(q, ω)=∑kfkfk+qεkεk+q+ω.】

【λsp=8πe2vFπn√ω2(1+εsub)】

Below the report platform, when Xu Chuan suddenly started to act, Tao Zhexuan, who was paying attention, suddenly held his breath and stared at the blackboards with full concentration.

Is his feeling going to come true?

But, what can he do this time?

Is it a phased result?

Or find a new method to include all strongly correlated electron systems?

He is not a scholar in the field of physics. Although he has studied extensively in the field of mathematics and knows some physics knowledge. But the knowledge on the blackboard involving cutting-edge physics still makes him a little confused.

On the other side, Edward Witten, who had sat down again, shrank his pupils slightly when he saw those lines of formulas, as if he had a premonition of something, but he didn't dare to believe his own judgment.

There is no other reason. If it is really it, it is really amazing.

Involuntarily, his breathing became heavier.

On the podium, Xu Chuan ignored the audience below, and the chalk in his hand continued to outline formulas on the blackboard in front of him.

The ideas in his mind supported him to move forward, and his research and ability in mathematical physics and materials science were his most powerful weapons at the moment, clearing a clear path for him to overcome obstacles.

At the same time, in the front row of the audience seats at the lecture hall.

Looking at Xu Chuan's back in front of the blackboard, and then looking at his friend Witten who stood up again in astonishment, Deligne cast an inquiring look at him.

"What is he doing?"

Witten's eyebrows were also tightly furrowed, staring at the blackboard motionlessly, his eyes moving with the companies listed on the layer, as if thinking along with them.

Without getting an answer, Deligne's eyes fell on Xu Chuan who was writing formulas on the blackboard.

Is this student of his a little too perverted?

Mathematics, physics, astronomy, materials, chemistry, quantum theory. Is there anything he doesn't understand?

I really don't understand how he can master so many fields at the age of only 25.

Even his mentor, Grothendieck, couldn't have done this when he was young, right?

On the podium, Xu Chuan stopped his actions until the formulas were written on several blackboards. He stared blankly at the blackboard covered with formulas standing there.

After a long time, he finally came to his senses, breathed a sigh of relief, and threw the chalk in his hand into the chalk box.

This was the second time he encountered such a situation. Because the area of ​​the blackboard was not enough, he was forced to interrupt the proof process.

Fortunately, he had caught that inspiration.

If nothing unexpected happens, he can make up the rest in the next few days.

Under the podium, looking at Xu Chuan, Professor Witten asked with a trembling voice: "Did you do it?"

Xu Chuan shook his head and said, "Not yet."

After a slight pause, he added: "But at least I found a direction that should be feasible."

Witten: "What direction?"

Xu Chuan smiled and said, "Dimension!"

After that, he left the podium and did not return to his seat, but left the venue directly.

PS: There is another chapter in the evening, but it probably won’t be posted before 12 o’clock. There will be one in the morning. Please give me your monthly vote!