Research starts with PhD students

Chapter 134 Zhang Shuo: Do ​​you want to discuss math with me? (Two chapters in one)

Before going to the capital, Zhang Shuo had been studying the simplified calculation problems of the fermion Hubbard model, but he was not focused on the research tasks. Most of his time he read various materials to increase his knowledge.

When you have enough understanding of the relevant knowledge, it will be much easier to use mathematical analysis to conduct research.

The task progress is now close to '70%', which is very fast.

This is also related to the research on numerical simulation of NS equations.

Some methodological frameworks and conceptual frameworks in numerical simulation of NS equations can also be used to simplify computational simulation of physical models.

The study of mathematical models and partial differential equations is different.

Partial differential equations, when studied from a mathematical perspective, are purely mathematical problems.

The mathematical model of physical phenomena must start with the understanding of the physical description.

Mathematical models are much more complicated than equations. Just to understand the meaning of the model requires a lot of understanding. Also, because the model is too complicated, it cannot be studied purely in a mathematical way.

Therefore, the study of simplified algorithms should start with the understanding of physics.

In the fermion Hubbard model, each parameter corresponds to a physical expression. If we start from the understanding of physics, it cannot be simplified any further.

That's the contradiction.

The model is too complex to be studied using purely mathematical methods, but it cannot be simplified further in the physical sense.

Zhang Shuo has found a clear direction and has conducted in-depth research, starting with the analysis of the Hamiltonian of the fermion Hubbard model.

The Hamiltonian is the sum of the kinetic energies of all particles plus the potential energy of the particles associated with the system. For different situations or numbers of particles, the Hamiltonian is different because it includes the sum of the kinetic energies of the particles plus the potential energy function corresponding to the situation.

The research itself is a simplification of the computational simulation, not a simplification of the fermion Hubbard model. Therefore, the research is focused on the Hamiltonian of the model, and the direction of consideration is also how to calculate in order to simplify the overall calculation process.

Understanding from a physical perspective, analyzing the Hamiltonian, considering computational issues, and so on, a series of studies have only one ultimate goal -

Numerical calculations!
The fermion Hubbard model can be simply understood as a description of the state of electrons in a superconductor.

Numerical calculation of the model, that is, to know the instantaneous state of electrons in the superconductor through calculation.

There have been many studies on the numerical calculation of the fermion Hubbard model internationally, including collective quantum Monte Carlo, tensor renormalization group, etc., which are all numerical analysis methods.

Zhang Shuo has read a lot of information. His research mainly focuses on two directions, one of which is computational simulation.

One is the numerical method.

In the study of computational simulation of NS equations, some method frameworks can be used to simplify the computational simulation of mathematical models, but the prerequisite is to complete the research on numerical methods.

So both are still a study.

Numerical method, that is, numerical solution of the fermion Hubbard model. There have been many similar studies, but there is no method that can simplify the numerical solution.

Zhang Shuo found a method and named it 'Multiple Infinite Discrete Analysis'.

Multiple infinite discrete analysis does not mean doing endless calculations, but enumerating calculations. The more calculations are done, the more accurate the numerical results of the analysis will be.

It's like finding the number closest to one.

After one analysis, the result was 0.9; after two analyses, the result was 0.99; after three analyses, the result was 0.999…

Endless, constantly approaching.

This will make the numerical method more accurate. If only approximate calculations are performed, the amount of calculation will be many times smaller, and the computational simulation will be simplified.

……

For a whole week, Zhang Shuo focused on the study of the fermion Hubbard model.

When you focus on research, coupled with the direction guidance brought by '氪币', the progress of the task will increase rapidly, and the progress has been increased to '91%'.

Zhang Shuo checks the progress every day. He feels that the growth is dull and even relatively slow.

"In one week, seven days, the progress increased by a little over 21%, which translates to only 3% per day."

"3%, equivalent to '6' research coins."

He was considering the study of the singularity problem of the NS equations.

The NS equation singularity problem requires 7000 scientific research coins. At a rate of six scientific research coins per day, it will take three years to complete.

Compared with the difficulty and influence of the NS equation proof, three years is not a long time, or even very short, but it is of course best to complete it in a short time.

"I'm still a little anxious..."

Zhang Shuo thought about it and shook his head. He had always done research very quickly, so the thought that a research project would take three years seemed very long.

He secretly reminded himself, "I should keep a calm mind and not always try to have a big meal at one go."

Zhang Shuo put down the work at hand, opened his mailbox and took a few casual glances, and found more than a dozen invitation emails.

Some of them were invitations from foreign universities and research institutions, inviting him to give lectures, inviting him to visit, and even saying bluntly that they hoped he could work there.

There are also some emails from domestic institutions, which are also invitations from scientific research institutions and universities.

It would be rude not to reply to such emails.

Zhang Shuo patiently wrote two versions of the reply email, one in Chinese and one in English, but the meanings were the same:

“Thanks for the invitation.

I have been very busy with work recently and have no time and energy to think about other issues.

I'm sorry and thanks again. ”

After finishing the emails, he replied directly in two batches, then half-lying in his chair and browsing his phone.

I hadn't noticed for a while, but his online account already has over 500,000 followers.

For an online account, having a million followers is a threshold.

Five hundred thousand followers is relatively small, but you have to know that his account rarely posts content. Since registration, he has only sent three messages in total, which can be directly classified as "inactive".

Even so, the number of followers continues to grow.

There are also a lot of new messages on the account, all of which are likes, reposts, and comments.

I haven’t sent you a private message.

Zhang Shuo has set his profile to only accept private messages from people he follows, and the only person he follows is Sun Xingli, so it is obviously impossible for him to receive a private message.

There are quite a few comments, all of which are messages left under the messages he sent.

He opened the new comment message interface and originally just wanted to mark the new message as read, but when he saw the inquiry at the top, he immediately became interested.

"Professor Zhang Shuo, can the method you studied in the calculation and simulation of the NS equation be used in complex mathematical models?"

This message came from a very ordinary account with a name just a long string of letters. There was no information on it, but since the person could ask this kind of question, it was obvious that he had some knowledge of the calculation and simulation methods of the NS equations.

Zhang Shuo gave a rhetorical reply, "For example?"

After he replied, he swiped the message on the square, but he didn't expect the other party to reply soon, "Fermion Hubbard model?"

Zhang Shuo was stunned for a moment, and immediately replied, "Are you researching this?"

The other party quickly replied, "It's not research, it will be used."

"can."

Zhang Shuo sent two words, and then added, "What kind of research is it?"

The other party replied, "Follow me and chat in private message!"

Zhang Shuo clicked the "follow" button, and the other party soon sent him a private message, revealing his identity: Su Zhiguo, a researcher at the Superconductivity Laboratory of the Chinese Academy of Sciences.

Su Zhiguo explained, "We study the relationship between the mechanism of unconventional superconductivity and the electron-electron spin interaction."

"The research is mainly focused on copper oxides, but it involves electron-electron spin interactions, so many experimental problems involve complex mathematical model calculations."

"The results of our simulations using large computers are very poor. It would be great if the fermion Hubbard model could also be simulated like the NS equations."

Su Zhiguo had left a message to Zhang Shuo just to ask a casual question, and now he was just chatting with Zhang Shuo for a few words, and he had never thought about what methods Zhang Shuo might have.

The computational simulation of the fermion Hubbard model is an academic topic in quantum computer research and also a super difficult problem at the international level.

Even if it is just a numerical solution, it is a research topic that needs to be discussed in international meetings, and more than one discussion meeting has been held in related research fields in China.

He attended the conference once, but gained nothing. He just summarized several existing numerical analysis methods. The analysis methods can only be used as research directions, but they do not mean that the solution can be found. Zhang Shuo did not give a clear answer. He just asked a few questions in an understanding manner, and then said, "The fermion Hubbard model is too complicated. It is difficult to perform large-scale computational simulations, but numerical solutions may be available soon."

"hope so."

Su Zhiguo didn’t think about the research at all, he just felt that Zhang Shuo was comforting him.

After chatting with Su Zhiguo for a few sentences, Zhang Shuo was in a good mood because he found that his research could be directly applied in the field of superconducting mechanism research.

He closed the private message page and found a few more messages in the comments.

The new information came from a blogger named "Dr. Novelty" below his chat with Su Zhiguo.

"Can the method used in the computational simulation of the NS equation be used in the computational simulation of the fermion Hubbard model?"

"Professor Zhang Shuo, you said above that this might be what you were referring to, right?"

"Doesn't that mean that the computational simulation of the fermion Hubbard model can be simplified?"

"As far as I know, this is impossible!"

Zhang Shuo felt confused when looking at the messages. He clicked on the other party's profile and found that he was an online blogger with millions of followers. The messages he posted were all popular science about cutting-edge scientific research, and there were also several interview videos with various scholars.

He thought for a moment and gave an interrogative reply, "Do you want to discuss computational mathematics with me?"

He was asking sincerely.

The other party seems to be here to discuss mathematical problems, and if there are any differences in understanding of computational mathematics research, we can indeed discuss them.

'Dr. Novelty' is a middle-aged man in his forties named Yang Chao.

Yang Chao is a PhD in physics. After working for a few years after graduating with his PhD, he quit his job and started his own media. He quickly attracted a large number of fans by publishing unique cutting-edge technology content and interviewing scholars in cutting-edge technology research and development.

As a technology blogger, it’s natural for me to pay attention to the rising talent Zhang Shuo.

He accidentally noticed the conversation between Zhang Shuo and an ordinary account. After learning the content, he searched it online and then asked those questions.

Yang Chao didn't expect Zhang Shuo to give such a reply, "Do you want to discuss computational mathematics with me?"

Zhang Shuo's tone was inquiring, but reflected in the text it seemed a bit sarcastic.

Yang Chao suddenly felt that he was being despised.

What do you mean?
Does that mean I'm not qualified to discuss math with him?

As a technology blogger with millions of fans, Yang Chao thinks he is of some standard. Many people admire his breadth of knowledge, and many fans admire him very much.

result……

Don’t you even have the qualifications to discuss math problems with Zhang Shuo?

The more Yang Chaoyue watched, the angrier she got. She simply took a screenshot and posted it on Weibo, adding a sentence:

“Although Master Zhang Shuo said so.

But I still insist that the computational simulation of the fermion Hubbard model cannot be simplified at all! "

This sentence is very interesting.

He did not even mention the fact that he was "despised" and continued to dispute academic issues with Zhang Shuo.

After the message was released on Weibo, many fans left comments quickly, but ordinary people don’t understand math problems at all, and the opinions they expressed were just about which side they supported.

“Isn’t this just riding on the popularity of Zhang Shuo?”

"You are indeed not qualified to discuss math problems with Master Zhang Shuo. Do you have any questions?"

"To show off my popularity, I unfollowed you!"

"I don't care about model calculations, but when it comes to computational mathematics, only Master Zhang Shuo has the say, right?"

Of course, there are also many people who support Doctor Strange, saying, "The blogger is still quite capable!"

"Master Zhang Shuo's reply is a bit rude!"

"I don't understand this model. Why would such a problem occur during a normal chat?"

"You clearly look down on me in this tone!"

Some people support it, some people oppose it.

Looking at the various comments, Yang Chao suddenly had a new idea, "If I can prove that I am right, wouldn't it leave people with the impression that I am 'very powerful'?"

"Debating Zhang Shuo on an academic issue can increase the weight of professionalism..."

"It might become a hot topic and become more popular..."

As Yang Chao thought about it, his eyes lit up and he immediately bought a plane ticket to Xijing City.

After arriving in Xijing City, he contacted a professor at Xijing University of Science and Technology. Relying on his classmate relationship, he met Professor Huang Libo of Xijing University of Science and Technology the next day.

Huang Libo is the deputy director of the Institute of Quantum Computing at Xijing University of Science and Technology. His research project is "Building a quantum simulator to solve the fermion Hubbard model."

Yang Chao was introduced here. He is not a formal media reporter, but just a self-media internet blogger.

Huang Libo still felt very happy. Their research would never make it to the mainstream media, mainly because the research content was too obscure and any results would be difficult to be reported by the media.

It feels good to have an online self-media outlet that specializes in cutting-edge academic and popular science come to interview me, and I can also appear in online public opinion later.

So he was very cooperative and introduced the research content right away, "We are doing quantum computing research."

"With today's quantum computing technology, we can already study and solve some academic problems. Our main focus is the fermion Hubbard model. Our goal is to create a cold atom quantum simulator that can solve the fermion Hubbard model..."

"Ula Ula~~"

Huang Libo said a lot of things in a row, which gave Yang Chao a headache. However, he still listened patiently and nodded frequently as if he understood.

This also made Huang Libo feel very gratified.

There have been reporters who came to interview us before, but when we started talking about professional content, it was obvious that they didn’t understand.

This blogger has a PhD in physics and seems to be somewhat competent.

Yang Chao pretended to listen patiently and quickly started the questioning session. "Professor Huang, your research direction is to use quantum computing technology to complete the computational simulation of the fermion Hubberton model, right?"

"You could say the same thing."

Huang Libo nodded and corrected, "The difference is that the physical simulation is carried out by building a quantum simulator, and quantum technology is used for calculation in the process."

"This is very different from ordinary computer calculations."

Yang Chao quickly nodded in agreement and continued to ask, "As far as I know, the Fermion Hubberton model is a very complex superconducting model, so can its computational simulation be simplified?"

"For example, Professor Zhang Shuo completed a computational simulation study of the NS equation, which simplified the amount of calculation and the calculation method of the NS equation simulation. Can we use a similar method..."

Before he finished speaking, Huang Libo immediately shook his head and said, "You still don't understand!"

"Quantum computing is completely different from conventional computer computing."

"The fermion Hubbard model is extremely complex and cannot be simulated by conventional computers. Even numerical solutions are very, very difficult."

“If we can’t even solve it, how can we simulate it?”

"Quantum computing requires the construction of a quantum simulator in advance, that is, to enclose the physical phenomena in the quantum computing process, so that computational simulation can be performed. Do you understand what I mean?"

"Those computational mathematical methods cannot be used in the calculation of the fermion Hubberton model. Otherwise, we wouldn't have to make a quantum simulator, right?"

After Huang Libo finished speaking, Yang Chao immediately smiled. This was exactly what he wanted to hear.

The methods of computational mathematics cannot be used in the calculation of the fermion Hubberton model. Naturally, the calculation and simulation methods of the NS equations are also invalid.

Huang Libo is the most authoritative expert in the research direction of the fermion Hubberton model, and their research has been published in top academic journals.

We can always trust what Huang Libo says, right?
Yang Chao did not end the interview, but continued to ask several questions about the research.

After that, I returned to the hotel and started making the video immediately.

The video needs to be cut, of course.

He promised Huang Libo to put all the videos up, but the key questions and answers could be put at the front.

The following topics are all professional and academic, and netizens will not be interested in them at all.

(End of this chapter)