Chapter 475 The answer to the strongly correlated electronic system!
On the reporting table, Xu Chuan was stunned.
The voice of the narration stopped, and the audience in the audience was also stunned for a moment.
What's going on here?
Isn’t the report already completed? Why are you so stunned on stage?
Is there something wrong? Or something else?
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 with their peers 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 stage in a daze, no one bothered him, they just discussed and exchanged ideas in low voices 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 when he looked at the figure standing on the stage, an electric arc suddenly flashed in his mind, and the expression on his face suddenly became serious.
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 gifted by God to the mathematical community."
"perhaps......"
"Today we can see another miracle."
Hearing this, Schultz also remembered the video about the NS equation, smiled, and said: "Tao, maybe you are thinking too much."
Laughing, "It's just that kind of miracle and inspiration. You are lucky if you can do it once in your life. If you can do it every time, it would be 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 the environment he was in 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 influence 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 order of nanometers. 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, such as carbon nanotubes and one-dimensional graphene, which are one-dimensional materials.
Two-dimensional materials include the interface of 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, the lattice structure of the material, the electronic structure, and the spin arrangement.
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 strongly correlated electronic systems.
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, about ten minutes passed.
The crowd under the stage was much more noisy than before, but everyone still tried their best to maintain a quiet atmosphere. Since they were talking, they lowered their voices to avoid disturbing the thinking on stage.
By this time, the scholars in the lecture hall probably knew that this young expert seemed to have new inspiration.
Although the strongly correlated electronic system is not a problem in mathematics, everyone present is looking forward to some new breakthroughs.
After all, mathematics is the foundation of all natural sciences and the language of other subjects.
If physics is a subject that studies natural laws and logic, then mathematics itself is logic.
It is a thinking tool created subjectively by humans, and is a further simplified logic based on existing natural laws and logic.
The things that humans can currently reach within this cosmological constant are so limited, but mathematics has given infinite possibilities and brought infinite beauty to humans.
It belongs to Venus born in the bubble, and it also belongs to the aria on the G string. You can experience the vicissitudes of the coastline from natural fractals, you can also create a grand starry sky in a conservative chaotic system, and you can even create your own in vector space.
AI.
In the lecture hall, several students who came to attend the seminar with their instructors for the first time involuntarily clenched their fists, feeling a little worried and at a loss.
Although they were not standing on the podium in person, they seemed to feel the tension.
Of course, what they didn't know was that their mentor standing on the stage didn't feel any nervousness at all.
Time passed like this little by little, and I don’t know how long it had passed. The staff in the audience were hesitant to report to the leaders, reminding them that when the third report meeting was supposed to begin, Xu, who had not made any movement,
The river suddenly moved.
He turned around and took off the erasing board from the hook of the mobile blackboard, and wiped the blackboard clean in a few strokes.
Immediately, a white chalk point fell on the black panel, and lines of calculations quietly danced with the dance of the palm.
【x(q,w)=∑kfk?fk qek?ek q ?w....】
【λsp=8πe2vFπn???√?w2(1 esub)....】
Under the reporting table, when Xu Chuan suddenly started to take action, Tao Zhexuan, who was paying attention, suddenly held his breath and stared at the blackboards with concentration.
Are his feelings about to come true?
But, how far can he achieve this time?
Is it a phased achievement?
Or find a new way to incorporate all strongly correlated electronic systems?
He is not a scholar in the field of physics. Although he has studied extensively in the field of mathematics and understands some physics knowledge, the knowledge on the blackboard involving cutting-edge physics fields still makes him a little confused.
On the other side, Edward Witten, who had sat down again, his pupils shrank slightly when he saw those lines of calculations, as if he had a premonition of something, but he couldn't believe his own judgment.
If nothing else, it would be really amazing if it were true.
Involuntarily, his breathing became a little heavier.
On the reporting stage, Xu Chuan ignored the audience and continued to draw formulas on the blackboard in front of him with the chalk in his hand.
The ideas in his mind support him to continue moving forward, and his research and ability in mathematical physics and materials science are his most powerful weapons at this moment, helping him overcome obstacles and open up a clear path.
At the same time, in the front row of the auditorium in the lecture hall.
Looking at Xu Chuan's back in front of the blackboard, and then at his friend Witten who stood up again in shock, Deligne cast a questioning look at him.
"What is he doing?"
Witten's eyebrows were also furrowed tightly, and he stared at the blackboard motionlessly, his eyes moving along with the listed companies, as if he was thinking along with them.
When he didn't get an answer, Deligne's eyes fell on Xu Chuan, who was writing formulas in front of the blackboard.
Isn't his student 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 managed to become proficient in so many fields at the age of only twenty-five.
Even his mentor Grothendieck couldn't have done this when he was young, right?
...
On the reporting table, until all the formulas were written on several blackboards, Xu Chuan stopped what he was doing and stared blankly at the blackboard covered with equations standing there.
After a long time passed, he finally came to his senses, breathed a long sigh of relief, and threw the chalk in his hand into the chalk box.
This is the second time I encountered this situation. Because the blackboard area was not enough, I was forced to interrupt the proof process.
Fortunately, he had already caught that glimmer of inspiration.
If nothing else happens, he can make up for the rest in the next few days.
Looking at Xu Chuan in the audience, Professor Witten asked with a trembling voice: "You did it?"
Xu Chuan shook his head and said: "Not yet."
After a slight pause, he added: "But at least I have found a direction that should be feasible."
Witten: "What direction?"
Xu Chuan smiled and said: "Dimension!"
After that, he left the reporting table and left the venue directly without returning to his seat.
........
PS: There is another chapter in the evening, but it probably won’t be released before 12 o’clock. There will be one in the morning. Please vote for it!