The top student must be diligent

Looking at the equivalent equation written on the blackboard, everyone including Xiao Yi fell silent.

Is he really a genius?

"Just tell me whether it's right or not!"

Putting down the chalk, Liu Chao put his hands on his hips and said proudly.

Xu Ming was silent for a moment, then took the chalk and said: "The writing is very good, I will give you 100 points first."

Then he also wrote [100] on the blackboard.

However, Xu Ming changed the subject again: "But, 100 is equal to 100/1, so according to your generalized reduction method, we will divide the two 1s above and below, so your score is [00] ”

"You are the chicken belly and my cauliflower." Liu Chao gestured with his middle finger.

…

A small episode passed, which really made the atmosphere in the room lively a lot.

However, the results have not come out yet, so they will continue to wait for the time being.

Xiao Yi suddenly remembered something at this time, then opened his schoolbag, took out the books that Luo Mingya had given him, and handed them to Luo Mingya.

"Thank you for your books. I have finished reading these."

"Have you finished reading?" Luo Mingya was surprised, but she understood after a moment: "No wonder you were able to make these three models so quickly."

Xiao Yi smiled, but then frowned slightly and said, "But now I study density functional, first-principles calculations, molecular dynamics, Monte Carlo simulation and other methods."

"Obviously, they often face a trade-off between accuracy and computational effort when predicting material properties. Especially for complex material systems, the computational accuracy and efficiency of existing methods cannot meet actual needs."

In response, Luo Mingya nodded: "Yes, this is also an inevitable problem. There is no perfect method, and computational materials science is only a young science and still needs certain development."

Xiao Yi nodded slightly, and after thinking for a moment, he suddenly said: "Don't you think that one of the core problems is that we have not fully utilized the microscopic trajectories and laws of electron motion."

Luo Mingya sighed, "You are right. There are also discussions on this aspect in the field of computational materials science, but there are not many. It requires high mathematics and enough interdisciplinary knowledge."

But after Xiao Yi pondered for a moment, he spoke again: "Density functional theory essentially relies on the approximate exchange-correlation potential function, and the first principles calculation comes from the Schrödinger equation... If, I mean if."

"Using the path integration method in quantum mechanics, combined with the Markov chain Monte Carlo technique in probability theory, can we design a newer computational framework?"

Luo Mingya's beautiful eyes suddenly widened.

Chapter 145 It’s just a more difficult question

Hearing Xiao Yi's idea was really shocking to Luo Mingya.

Why was he able to have such insightful thinking after only studying computational materials science for such a period of time?

However, Luo Mingya didn't know how to answer this question for a while.

She is indeed a genius, otherwise she would not have been able to start this kind of project after only half a year of studying computational materials science.

But the same thing is that although she is talented enough, she is still within the normal range. She cannot think of an idea like Xiao Yi's.

After thinking for a moment, she said: "Can you explain specifically what the principle of your idea is?"

Xiao Yi nodded and said: "The core principle is to use the microscopic motion trajectory of electrons to accurately calculate the state function of electrons through the path integration method. This method can bypass the approximation of the exchange-correlation potential in DFT and directly calculate the electron's state function. interactions and overall behavior.”

"Then we introduced Markov chain Monte Carlo technology to optimize the calculation path and improve calculation efficiency."

“In this way, we can predict material properties through accurate predictions of electron behavior.”

"Basically, it combines the advantages of multiple methods including density functional theory, first principles calculations, Monte Carlo methods, etc."

After listening to what Xiao Yi said, Luo Mingya started thinking. After a moment, she nodded and said, "Anyway, if you ask me to speak from the perspective of materials science, your idea is completely credible."

“If we can really calculate the movement trajectories and patterns of electrons, it will certainly help us predict various properties of materials. After all, the different properties of different materials are ultimately reflected by the different distributions of electrons within them. "

"Just like Zhao Yuanyuan's experimental data that day, defects in the crystal lattice caused changes in the reaction."

Zhao Yuanyuan's head came over at this time: "Did I hear you guys mention me?"

"It's none of your business." Luo Mingya rolled his eyes at her.

"Well..." After a pause, she continued: "But no matter what, it is still a huge problem to achieve what you said. Let's briefly talk about path integrals. I have a certain knowledge of this. learn."

"You just said that the method of computational materials science requires a balance between calculation accuracy and calculation amount. However, the computational complexity of path integral is extremely high, especially when dealing with multi-electron systems, the amount of calculation is exponential. increase."

“So how do you control the amount of computation?”

Facing this question raised by Luo Mingya, Xiao Yi just smiled: "Use machine learning technology."

“I don’t know if you have heard of variational autoencoder technology, also known as VAE technology. This is a generative network structure based on variational Bayesian inference. When I am thinking about it these days, I will use this technology from By making some simple optimizations based on mathematical principles and incorporating them into the neural network through machine learning, the generated electron trajectories can be automatically optimized.”

"This not only reduces the amount of calculations, but also achieves high-precision requirements."

Listening to their conversation, Zhao Yuanyuan began to faint, and then quickly moved away from them. She felt like she had suffered an IQ nuclear attack.

However, Luo Mingya was no different from her.

The genius of the materials department finally heard something he didn't understand.

"VAE technology?" She thought about it carefully for a long time, and finally shook her head and said, "I have never heard of this. If it involves machine learning, it is indeed not within the scope of my professional study."

"However, I do know that applying machine learning to materials research has been a hot topic in the past two years, just like the two-dimensional materials we are currently studying."

"No matter what," Luo Mingya said: "This idea of ​​yours at least seems to be a good idea, although it may be very difficult to implement. Just as you said, it is necessary to convert the Markov chain into a montage. Carlo technology is introduced to optimize the calculation path, and I can almost imagine how difficult it is mathematically.”

"Not to mention your original idea of ​​how to establish the relationship between path integrals and electron orbits."

"How to achieve these points, I guess I won't be able to help you. Maybe you can find that woman Sun Lina... But I don't think she knows much about it. Her math is worse than mine."

As he spoke, Luo Minya expressed his envy for the first time: "To be honest, sometimes I really envy you mathematicians for being able to master mathematics so thoroughly. For those of us who study other subjects, I really can’t understand what kind of state of thinking that is. No matter how much I studied mathematics, I could never reach that state.”

Looking at her expression, Xiao Yi smiled and said gently: "That's because you can do all kinds of things well enough even if you don't need to learn mathematics well. There is no need for anyone to stick to a certain The same is true for things and life.”

After hearing Xiao Yi's words, Luo Mingya was quiet for a long time, and finally took a deep look at Xiao Yi and said, "Thank you, I understand."

Xiao Yi was stunned for a moment, then waved his hand and said with a smile: "You're welcome. As a person who studies mathematics, it is necessary to provide such explanations to those who are confused about mathematics."

"I think you are different from other people who study mathematics. You are a gentle mathematician." Luo Mingya said.

"Really?" This compliment caught him off guard, Xiao Yi said slightly shyly: "Then thank you for the compliment."

Luo Mingya smiled and then said: "No matter what, if you plan to study the ideas you just mentioned, if you have any materials science problems, I can help you to the best of my ability. In addition, I can help you to the best of my ability." , you just said that machine learning may also be needed, which should require a large amount of data, and I can provide it to you.”

Xiao Yi nodded: "Thank you very much."

At this moment, Xu Ming shouted: "The results are out!"

Xiao Yi and Luo Mingya turned to look, and the latter walked over immediately. Soon, her eyes lit up.

"So that's it!"

"Comparable band structures are found for the 2H and 2H/3R polytypes, with the valence band top of the 2H/3R polytype being at a high symmetry point...so the volume plasmon peaks for all polytypes occur at similar energy loss value.”

"In this way, we can further determine the energy loss intensity of different valence bands and conduction bands in different energy loss regions."

"Great! Now we are one step closer to the final conclusion!"

Luo Mingya clapped his hands and said: "What we have to do next is very simple. Look for those heterostructures based on TMD. Now go back to the laboratory!"

Then, she took her junior brothers and sisters and left here. Before leaving, she said to Xiao Yi: "There should be nothing to do with you from now on. You can study your idea with peace of mind."

"I will contact you when our project is completed. Your position will be indispensable by then."

Then, she left with the people.

Xiao Yi watched them leave and raised his eyebrows.

In other words, the next topic has nothing to do with itself?

Okay, that way he can focus on his research.

By accurately predicting the trajectory and rules of electrons in materials, a new theoretical model can be constructed...

Sitting back in his original position, he took out the scratch paper he had used during this period and reviewed the previous relevant derivation.

On the first piece of draft paper, there is a line like this: [Absolute Electronic Computation (AEC)]

This is the name he gave to this method.

All materials need to follow the principle that the chemical bonds between atoms are formed by electrons, and these chemical bonds form the most basic structure of the material.

The properties of the material are also derived from this point, nothing more than this.

Just like the saying, structure determines properties, and properties determine functions.

For example, there is a material technology called single crystal casting technology, which can make the material only have a single crystal structure, which means that the atomic arrangement inside the entire casting is continuous and there are no grain boundaries, so it can make the material have extremely strong mechanical properties and creep resistance, especially in high temperature environments, so it is also widely used in the field of aviation engines, such as turbine blades.

And the absolute electronic calculation is to predict the behavior of electrons, so as to calculate the structure of electrons, and then predict the properties of materials.

However, how to predict the behavior of electrons, first of all, the path integral must be quoted.

[qf, tf|qi, ti=∫D[q(t)]exp(iS[q(t)])]

Write the formula of the path integral on the draft paper.

Xiao Yi knocked his head.

Unlike the Schrödinger equation, the path integral method calculates the behavior of a quantum system by summing up all possible quantum paths. This method is particularly suitable for dealing with multi-body problems and strongly interacting systems.

So obviously, in terms of predicting material properties, the path integral has a very good effect on this.

"In addition, in electronic structure calculations, the path integral method can be used to calculate the distribution function and correlation function of particles, especially when dealing with electronic correlation effects and thermal effects."