Chapter 461: The scientific research intuition of a young genius
In the living room, Xu Chuan and Mr. Yang exchanged some research directions on strongly correlated electronic systems.
It has to be said that although this old gentleman is nearly a hundred years old, his thinking is still quite clear and he can filter and eliminate many directions based on the knowledge in his mind.
This is extremely rare for a centenarian.
For Xu Chuan, although these exchanges are only about research directions and theories, they can still save him a lot of time and point out some directions, which is a big gain.
On the side, Qiu Chengtong, who was listening to his exchange with Mr. Yang, suddenly interjected: "Although condensed matter physics is not within the scope of my research, why don't you regard the behavior of electrons in strongly correlated electron systems as electronic liquids or electronic solids?
"
"Such as Rattinger liquid, liquid crystal state, charge density wave, Wigner crystal, etc. Perhaps this explanation can achieve the purpose you mentioned?"
"E-liquid?"
Mr. Qiu suddenly interrupted, causing Xu Chuan to look over in confusion.
I saw this old man famous for mathematics continue to explain: "Although my main research direction is not physics, I know that based on the idea of topological core rotation, the unified mathematical theory of quantum liquids has been developed. Including topological order,
"If you could explain the topological skeleton and local quantum symmetry of quantum liquids, and show that all n quantum liquids form a ?-condensate complete higher category, the equivalent type of which can be calculated explicitly by a simple co-chip 1-category, maybe
Can you do what you need?"
"Starting from the field of quantum liquids?"
These words made Xu Chuan stunned for a moment and fell into thinking.
The strongly correlated electronic system comes from the interaction of electrons. Without interaction, there is no correlation between the movements of electrons.
To put it simply, a strong interaction means a strong correlation, and a weak interaction means a weak correlation. The "strong" and "weak" here refer to the relative size, not the absolute size, and depend on the competition between different energies within the system.
The same interaction has different effects on half-filled energy bands and full bands, or on massive electrons (flat-band electrons) and massless electrons (Dirac fermions).
In condensed matter physics, the behavior of the electronic system can usually be regarded as a gas (free electron gas).
The "electrons" here can be quasiparticles, such as conduction band electrons in crystals, or single-particle excitations of other interacting systems—that is, they are originally liquids, but they can still be regarded as gases through simple approximations.
After all, when the interaction is small, it can be approximated by free electrons; when the interaction is large, a Mott insulator will be formed, and the degree of freedom of electron motion is frozen, leaving only the degree of freedom of spin.
At this time, an effective spin model can be obtained by unfolding it with a large degree of freedom...
From this perspective, it is indeed feasible to treat the locked electron movement in the strongly correlated electron system as a liquid or solid.
However, he couldn't figure out how to take this road for a while.
After all, it often takes a long time to go from idea to research.
...
On the other side, in the living room, Mr. Yang and Mr. Qiu did not disturb Xu Chuan who was deep in thought, each thinking about other directions and ideas.
The purpose of today's exchange on strongly correlated electronic systems is to provide some ideas and directions for the young scholar in front of me, and they can still do this.
As for more specific calculations, I'm afraid he has to rely on himself.
Whether it is Mr. Yang or Mr. Qiu, at their current age, it can be said that they no longer have the energy to complete such top-notch and cutting-edge calculations.
Even in the past two years, Mr. Qiu still had the energy to study and advance the difficult problem of the KZB equation.
But as year after year passes, people age faster and faster.
Science is always young, and they, the old people who are sunsetting, are no longer able to advance new knowledge.
...
In the living room, Xu Chuan pondered for a long time before coming back to his senses.
Seeing him making any movement, Mr. Qiu looked over first and asked curiously: "How is it?"
Xu Chuan thought for a while and said: "There is a little idea. As for whether it can be done, we will have to study it later. I would like to thank you both for your ideas and theories today. I am really sorry to trouble you."
Mr. Qiu smiled and said: "This is no trouble, as long as it helps you."
After a slight pause, he continued: "Of course, I am not very familiar with the direction of physics. There is no need for you to insist on the theory I proposed. Maybe it is wrong."
He was taking a precaution in advance to prevent Xu Chuan from striving in the direction he proposed. After all, he was not a pure physicist, and condensed matter physics was not within the scope of his research.
Xu Chuan smiled and nodded, saying: "Don't worry, I have never been someone who sticks to one path. When I feel that this path is not going to work, it is most likely that I will give up on it."
"But now, I think I can still give it a try. At least I think it should be feasible. I feel like I can see the end."
Opposite me, Mr. Yang seemed to have remembered something and suddenly said: "Is this the scientific research intuition of a genius when he was young?"
After a slight pause, he continued: "When I used to study the Yang-Mills equation, when I tried to extend gauge invariance to non-commutative groups, I tried many methods, but failed many times."
"Because U1 symmetry is commutative symmetry and SU2 symmetry is non-commutative symmetry, I was stuck for a long time. Until one time when I decided to add a quadratic term, I only had this idea at the time, and I couldn't help but think
I got the idea that this is the right path.”
"It was soon confirmed that this idea was correct, and a new field theory was successfully introduced."
After a pause, he then sighed: "It's a pity that in the subsequent research, I almost never had this kind of unusual clarity, as if I can see the correct answer as soon as I come up with an idea."
As he spoke, he looked at Xu Chuan, asking and describing: "I used to never understand why you could make such brilliant achievements at this age, but now it seems that you can often have this kind of intuition when studying problems.
?”
Hearing Mr. Yang's emotion, Xu Chuan was stunned for a moment.
Does he seem to have this kind of intuition?
And it's not just once or twice. When he was studying mathematics before, whether he was studying Hodge's conjecture or NS equations, he could always rely on this feeling at key points to judge whether the next path was appropriate.
Of course, it is unrealistic to say that the correct answer can be seen at a glance.
But indeed, this feeling helped him save a lot of time.
In the past, he always felt that this was a judgment brought by the knowledge in his mind. Now when Mr. Yang talks about it, it seems to be a little different?
On the side, Mr. Qiu said with a smile: "Don't listen to his nonsense, what scientific intuition, what he talks about is so metaphysical, and what he talks about is just the experiential feeling brought by knowledge."
"Those people who are engaged in physics have all developed towards theology in the end. This old guy has had this trend a few years ago. You kid, don't listen to his deception, just do your own research seriously.
If this idea is reliable, sows will climb trees."
Hearing this, Xu Chuan coughed in embarrassment.
He seems to be into physics.
.........
PS: Second update, please give me monthly tickets.
Ahem, it was supposed to be the third update today, but I found that I overestimated my own strength. It took me a lot of time to look up information and understand the papers today. I’ll make up for it later. ˋ(°▽,°)
