Chapter 460 The Scientific Research Intuition of a Young Genius

In the living room, Xu Chuan and Mr. Yang exchanged some research directions of strongly correlated electron systems.

It must be said that although this old man is nearly a hundred years old, his thinking is still quite clear, and he can rely on the knowledge in his mind to screen and eliminate many directions.

This is extremely rare for a centenarian.

For Xu Chuan, although these exchanges are only some research directions and theories, they can still save him a lot of time and point out some directions, and the gains are not small.

On the side, Qiu Chengtong, who was listening to him and Mr. Yang’s communication, suddenly interrupted and said: "Although condensed matter physics is not within my research scope, why don’t you regard the behavior of electrons in strongly correlated electron systems as electronic liquids or electronic solids?"

"Such as Luttinger liquids, liquid crystal states, charge density waves, Wigner crystals, etc., perhaps from this aspect, you can achieve your purpose?"

"Electronic liquid?"

Mr. Qiu suddenly interrupted, making Xu Chuan look over in confusion.

The old man, who was famous for mathematics, continued 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, SPT/SET order, symmetry-breaking order and CFT-like gapless phase, etc."

"If you can explain the topological skeleton and local quantum symmetry of quantum liquids, and show that all n quantum liquids form a -condensed complete higher category, whose equivalent type can be explicitly calculated by simple copiece 1-category, maybe you can do what you need?"

"Starting from the field of quantum liquids?"

This made Xu Chuan stunned for a moment and fell into thought.

The strongly correlated electron system comes from the interaction of electrons. Without interaction, there is no correlation between the movements of electrons.

Simply put, the stronger the interaction, the stronger the correlation, and the weaker the interaction, the weaker the correlation. The "strong" and "weak" here refer to relative size, not 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 electronic systems can usually be regarded as 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, it is originally a liquid, but it can still be regarded as a gas through simple approximation.

After all, when the interaction is very small, it can be approximated by free electrons; when the interaction is very large, a Mott insulator will be formed, and the freedom of electron motion will be frozen, leaving only the freedom of spin.

At this time, a large degree of freedom can be expanded to obtain an effective spin model.

If you look at it from this perspective, it is indeed feasible to regard the locked electron motion in a strongly correlated electronic system as a liquid or solid.

However, he couldn't figure out how to go this way for a while.

After all, it often takes a long time from ideas to research.

On the other side, in the living room, Mr. Yang and Mr. Qiu did not disturb Xu Chuan, who was lost in thought, and each thought about other directions and ideas.

Today's communication on the strongly correlated electronic system aims to provide some ideas and directions for the young scholar in front of them, which they can still do.

As for more specific calculations, I'm afraid he will have to rely on himself.

Whether it is Mr. Yang or Mr. Qiu, at their current age, it can almost be said that they no longer have the energy to complete such top-level frontier calculations.

Even in the past two years, Mr. Qiu still had the energy to study and advance the KZB equation problem.

But as the years go by, people age faster and faster.

Science is always young, and these old people who are in their twilight years 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 move, Mr. Qiu looked over first and asked curiously, "How is it?"

Xu Chuan thought for a while and said, "I have some ideas, but whether it can be done or not, we need to study it later. I am very grateful for your ideas and theories today. I really trouble you."

Mr. Qiu smiled and said, "It's not a big deal. It's okay as long as it helps you."

After a slight pause, he continued, "Of course, I'm not very familiar with the direction of physics. You don't have to stick to the theory I proposed. Maybe it's wrong."

He was taking precautions in advance to prevent Xu Chuan from sticking to the direction he proposed. After all, he was not a pure physicist, and condensed matter physics was not within his research scope.

Xu Chuan smiled and nodded, saying, "Don't worry, I'm not the kind of person who sticks to one path. When I feel that this path is not feasible, it is most likely that I will give it up."

"But now, I think I can still give it a try. At least I think it should be feasible. I feel that I can see the end."

On the other side, Mr. Yang seemed to remember 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 was studying the Yang-Mills equations before, I tried to generalize the gauge invariance to non-commutative groups. I tried many ways, but failed many times."

"Because U1 symmetry is a commutative symmetry and SU2 symmetry is a 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 that this path was right."

"Later, this idea was soon confirmed to be correct, and the new field theory was successfully introduced."

After a pause, he continued with emotion: "It's just a pity that in the subsequent research, I almost never had this unusually clear feeling, as if I could see the correct answer as long as I had an idea."

As he said, he looked at Xu Chuan, asking and explaining: "I always couldn't figure out why you can make such brilliant achievements at this age. Now it seems that you can often have this intuition when studying problems?"

Hearing Mr. Yang's sigh, Xu Chuan was stunned.

It seems that he also has this intuition?

And it's not just once or twice. When he was studying mathematics before, whether it was studying the Hodge conjecture or the NS equation, he could always rely on this feeling at key points to judge whether the subsequent path was appropriate.

Of course, it is unrealistic to say that you can see the correct answer at a glance.

But it is true that this feeling helped him save a lot of time.

In the past, he always thought that this was a judgment brought by the knowledge in his mind. Now, after listening to Mr. Yang, it seems a little different?

On the side, Mr. Qiu smiled and said, "Don't listen to his nonsense. What scientific intuition, so metaphysical, is just an empirical feeling brought by knowledge."

"This group of physicists have finally developed towards theology. This old guy has had this trend in the early years. Don't listen to him, just do your own research seriously. If this idea is reliable, sows will climb trees."

Hearing this, Xu Chuan coughed awkwardly.

He seems to be a physicist.

PS: Second update for monthly tickets.

Ahem, originally said that I would update three times today, but I found that I overestimated my ability. It took a lot of time to check the information and understand the paper today. I will make up for it laterˋ(°▽、°)