Chapter 159: Can the update speed be faster?
The problem has been found though.
But there is still no clue on how to solve the problem.
It is to further seek optimization solutions based on the original methods.
Or is there any better method to further reduce the error and obtain the ideal numerical result?
Xu You doesn't have any good solution for this at the moment.
"Teacher, I'll think about it when I get back and see if there's a better approximation method. Can you give me a copy of this paper? I promise I won't share it with anyone else."
Wang Xiangwu and Zhao Weijia both trusted Xu You very much and readily agreed to his request.
"Of course, just copy it. If you have any other questions, you can always contact me."
Since Wang Xiangwu has taken the initiative to ask Xu You for help, he naturally would not distrust Xu You.
After returning from Wang Xiangwu’s laboratory, Xu Youxian returned to the dormitory.
Of course I went to pick up the suitcase.
Although we are trying to find ways to solve the problem, if we do not have enough knowledge, just thinking is definitely not enough.
Xu You still needs to further supplement his knowledge in related areas.
Seeing Xu You coming to the library, the library staff all saluted him at the same time.
Three full days had passed since Xu You last came to the library.
Originally, Xu You would come to the library every two days.
Xu You also nodded to the staff members.
There was no way. Xu You came too often and had become familiar with them.
Because Xu You rarely attends classes and rarely participates in various activities in the college.
Xu You is even more familiar with the library staff than with many of his classmates in the college.
Carrying his precious suitcase, Xu You began to search the library again.
When Xu You has read a certain number of books.
A new problem also emerged.
That is, Xu You has read many books.
The speed at which the library's books are updated is really not as fast as Xu You's reading speed.
It was becoming increasingly difficult for Xu You to find a good book that he had never read before.
After coming out of the library, Xu You once again felt the gazes of the library staff.
Xu You looked at the librarian, seeming to want to say something but stopping himself.
"What's wrong, Xu You, is there any problem?"
Librarians also pay special attention to the library's largest customer.
"Teacher, I have something to say, but I don't know whether I should say it or not."
"Student Xu You, please speak quickly."
"Can the update speed of books in our library be a little faster? I'm starting to run out of books."
The librarian thought, no matter how fast the updates are, they won’t be enough for you to read.
Sometimes, it’s not a matter of money, but there really aren’t that many new books.
"Okay, Xu You, I will help you report this matter."
"Okay, thank you teacher."
After returning to the dormitory, Xu You sorted out the books and began a pleasant reading session.
Xu You has two ways of selecting books.
One is to look at some knowledge that may not be used for the time being, but may be used in the future, as a reserve of knowledge.
Another way is to look at some of the knowledge that is currently involved, like we are doing now.
On this issue, Xu You also believes that approximate methods must be applied.
How to minimize the error caused by approximation to the greatest extent is the most critical issue.
"Hmm? Mean field approximation?"
At this time, Xu You suddenly discovered such a method.
In fact, Xu You had heard of this method before, but he had never really studied it in detail.
And this time, Xu You felt that this method was likely to be applied to this problem.
The mean field approximation is often used to study complex multi-body problems.
The problem of a huge number of interacting multi-body bodies can be transformed into a single-body problem in which each particle is in a weak periodic field.
Although there has been no application of this method to similar problems.
But Xu You thought it was still worth a try.
"It won't work if you just put it in, you still need to optimize it ."
Xu You opened the paper and optimized the method according to the characteristics of the research problem.
There are many formulas involved in this problem, so it is very complicated to deal with.
"Starting from the basic interaction between the two-level system and the light field. The anti-rotation wave term will decay rapidly to zero as it evolves in time, and this can certainly be ignored..."
Xu You deduced the formula step by step, being extremely careful with every step.
"Huh~ I finally figured out the Hamiltonian."
In this way, we can finally start applying the mean field approximation .
"First, introduce a superfluid order parameter..."
Because the Hamiltonian obtained previously is very difficult to calculate specifically.
Xu You must use an approximate method to calculate it while maintaining extremely high accuracy and reducing errors as much as possible.
After another series of calculations, Xu You finally completed further derivation.
"The high-order fluctuation terms here can be ignored under the mean field approximation. In this way, the effective Hamiltonian can be calculated."
After finishing the last formula, Xu You could finally breathe a sigh of relief.
Xu You didn't know whether anyone had used this method to solve similar problems before him.
But according to Xu You's feeling, this new method will greatly reduce the error.
"Substitute the data to verify it."
Although Xu You's feelings are usually very accurate.
However, further verification is still needed to finally prove whether the method is appropriate or not.
Xu You input the effective Hamiltonian expression he had just derived into the software and started the fitting work again.
Looking at the newly emerging curve, which was closer to the theoretical curve, Xu You knew that his method should be correct.
"Sure enough, this kind of error is a more ideal data!"
In order to ensure the applicability of this method, Xu You examined several other sets of data and further confirmed his ideas.
"This way, the problem should be solved."
This time, Xu You took less than half a day.
I haven’t even finished reading half of the books I just borrowed.
Xu You couldn't care less and quickly took his computer and draft paper back to Wang Xiangwu's laboratory.
Seeing Xu You coming back, Zhao Weijia asked:
"What's wrong, Xu You, do you need more data?"
Zhao Weijia subconsciously thought that Xu You came back to ask for it because he did not have enough information or data.
"No need. Brother, call Teacher Wang over. I have found a better approximation method."
