Chapter 472 Deligne: How Can I Understand This?

Chapter 472 Deligne: How can I understand this?

Hearing his friend's question, Witten took a deep breath and slowly calmed down.

Looking at the silver-white curtain on the podium, he said: "You are a pure mathematician. It may be difficult for you to understand the influence of the mathematical foundation theory of non-equilibrium strongly correlated electron system on condensed matter physics."

"If you ask me to evaluate, the difficult problems in the strongly correlated electron system are as important in condensed matter physics as the Riemann hypothesis in number theory."

"In two different systems, it may be difficult to compare the difficulty of solving them separately. But the influence is not weak at all."

"And the non-equilibrium strongly correlated electron system is the most classic one among the difficult problems of the strongly correlated electron system. It studies the dynamic behavior of the strongly correlated system in the non-equilibrium state to reveal new physical phenomena and application potential."

"But not only until now, no one in the physics and mathematics circles can give a perfect mathematical foundation, or even a perfect mathematical tool."

Witten explained briefly, but his eyes never moved away. He kept staring at the podium, and his inner unrest appeared on his face, which surprised Deligne.

Having worked with this friend at the Institute for Advanced Study in Princeton for so many years, he rarely saw Witten lose his composure like this, especially as he got older.

However, after listening to the explanation, he understood a little.

If the influence of a difficult problem can be compared with the Riemann hypothesis in mathematics, then this difficult problem will inevitably have a very high reputation and influence in the corresponding field.

Just like the Riemann hypothesis, with the development of mathematics in recent years, there are thousands of mathematical formulas based on the establishment of this hypothesis.

If the Riemann hypothesis is proved to be true, then these thousands of formulas will be promoted to theorems together with it.

If it is disproven, the field of number theory will follow with the biggest earthquake in history.

If the influence of the field of strong correlation on condensed matter physics can reach this level, it is no wonder that Witten is so surprised.

Even if only a part of the results can affect the development of condensed matter physics.

In fact, Deligne's thinking is still too simple.

Compared to Witten, he is really a pure mathematician, mainly engaged in research in algebraic geometry and number theory, and has never been away from mathematics in his life.

He really doesn't know much about physics. Although he knows condensed matter physics and strongly correlated electron systems, he is not clear about the specific influence of these two in condensed matter physics.

Even Edward Witten did not say how much influence the strongly correlated electron system has.

After all, his main research scope does not include condensed matter physics, and he only knows about it because of mathematical physics and quantum theory.

In fact, the influence of strongly correlated electron systems in the field of condensed matter physics and even the entire field of physics is one of the largest branches.

The correlation of electrons can lead to a large number of rich quantum effects and phenomena such as high temperature, unconventional superconductivity, abnormal magnetism, metal insulator phase transition, semimetal, giant thermoelectricity, multiferroicity, heavy fermions, etc.

And exploring the microscopic mechanism of these effects and phenomena and establishing a multi-body quantum theory system is one of the most active and challenging frontier research fields in condensed matter physics, quantum physics, chemical physics and other directions.

Perhaps the strongly correlated electron system described by the Riemann hypothesis is not a very appropriate explanation.

If we really want to use mathematics to find an approximate problem, then the NS equation should be the most similar.

The advancement and solution of the NS equation will greatly enhance human understanding of fluids, thereby bringing about tremendous development in all theories and technologies related to fluids.

From simulating cloud flow, ocean flow, turbulence after airplane takeoff, flow resistance after rocket launch, to blood flow through the heart and other fields.

All will be greatly improved.

For the strongly correlated electron system, the solution of this whole set of systematic problems will make human understanding of condensed matter physics and microscopic particles a qualitative leap.

And this field affects the development of materials.

For example, the hottest copper-based/iron-based superconductors, FeSe/STO interface superconductors, iridium oxides, Mott insulators, quantum antiferromagnets and other low-dimensional quantum new materials in recent years are all born under the strongly correlated electron system.

And the emergence of each of these materials has made human technology take a big step forward, and its significance is naturally self-evident.

At the podium, Xu Chuan opened the PPT and turned to a new page.

"For us, mathematics is a discipline that studies concepts such as quantity, structure, change, and spatial models."

"Through the use of abstraction and logical reasoning, it is generated from counting, calculation, measurement, and observation of the shape and movement of objects. We expand these concepts in order to formulate new conjectures and establish rigorously derived truths from appropriately selected axioms and definitions."

"And these truths are applied to other fields, bringing technology and progress to mankind."

"What I want to talk about today is the use of mathematical tools to bring a set of mathematical theories and calculation methods to the strongly correlated electron system in condensed matter physics, which can greatly promote the development of condensed matter physics and particle physics."

"Of course, in turn, with the development of physics, it is bound to drive the progress of mathematics."

"Just like Newton invented calculus to solve physical problems. Faraday studied electricity and magnetism, but due to his limited mathematical level, he was unable to further provide a profound connection between electricity and magnetism, while Maxwell used his superb mathematical talent to perfectly unify electricity and magnetism."

"After all, we always need mathematics to explain these new phenomena and theories."

As he spoke, Xu Chuan flipped through the PPT.

"Okay, next I will give a report on my paper from the basics to the advanced."

"First principles calculation is based on the principle of interaction between atomic nuclei and electrons and their basic laws of motion, using the principles of quantum mechanics, starting from specific requirements, and after some approximate processing, directly solving the Schrödinger equation"

"Both ab initio calculations based on Hartree-Fock self-consistent field calculations and density functional theory (DFT) calculations are included in this category."

"For example, φM=-(Ve+εFe)."

"I believe that even if you have not studied physics, you can see that this is the minimum work value required to calculate the Fermi energy level of metal M to extract electrons across the surface without net charge."

"."

On the report platform, as Xu Chuan explained, lines of formulas were presented to everyone.

For the mathematicians sitting here today, as time goes by, not everyone can keep up with the pace and understand these things smoothly.

But in the lecture hall with hundreds of people, there are many top mathematicians and scholars in the field of mathematical physics, such as Edward Witten, Mr. Qiu, Deligne, etc.

These people were listening attentively.

The calculation of first principles is not difficult to understand for the mathematicians present. After all, it is a principle of the basic properties of the ground state of the system that is calculated from scratch using mathematics. It does not require any experimental parameters, but only some basic physical constants.

But as time goes by, not many people can keep up with the pace.

For Xu Chuan, he did not expect to make everything related to physics clear to everyone at today's mathematics seminar.

What he did was to tell many mathematicians about the application of mathematics and the relationship between mathematics and physics in this process.

Compared with mathematicians like his mentor Professor Deligne, he is actually far less pure.

If possible, he hopes that more mathematicians can enter the field of physics. Of course, he also hopes that more physicists can accept more new mathematical knowledge.

Physics is a science that understands nature and gives an abstract description of the real world, while mathematics is the language of science. Neither of them can be separated from the other.

In the front row of the audience, watching Xu Chuan standing on the podium and reporting, Professor Deligne couldn't help but poke Witten beside him: "What is he doing?"

In the second half of the report, he could no longer understand what his student was saying.

For a top mathematician like him, this feeling was too hard to accept.

Professor Witten stared at the podium without turning his head and said, "To put it simply, he is using mathematics to explain the non-equilibrium strongly correlated electron system. Just like Einstein used Riemann geometry to describe gravity."

"What he is doing now is using mathematics to describe the non-equilibrium strongly correlated electron system."

Deligne was silent for a moment and asked, "How can I understand this?"

Hearing this, Edward Witten came back to his senses, thought for a while, and said, "Maybe you need to learn some knowledge of condensed matter physics?"

After a slight pause, he added, "Maybe you need some knowledge of quantum chemistry, quantum many-body physics, atomic and molecular physics, etc."

"But it is probably too late. The things he reported today have already involved the most cutting-edge condensed matter physics. Even for me, it is not so easy to understand."

Deligne: "."

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