Chapter 473 The Final Answer

The report will continue.

Regarding today's report, Xu Chuan did not make a very detailed report.

After all, today's seminar is for the mathematics world, not the physics world.

Although mathematical methods are used to explain non-equilibrium strongly correlated electronic systems, it is estimated that few people in the lecture hall can understand these things.

After all, this is content in the field of physics.

Perhaps a few people such as Witten and Qiu Chengtong can fully understand his report, but it does not mean much to the entire method and paper.

This kind of thing must eventually be recognized by the entire physics community.

".Consider the second variable of a two-variable function f(x1, x2) in a complete set of single-variable basis functions {φi(x)}i=1^N. Expand f(x1, x2)=∑^ni =1bi(x1)φ(x2), the obtained coefficient bi(x1) is a function of the first variable.”

"The basis function is further expanded to."

“f(x1, x2)=∑^ni＞JCij[φi（x1）φj(x2)-φi（x1）φJ（x2）]=∑^ni＞J|φi（x1）φi（x2）/φj（ x1)φj(x2)|”

"From the above formula, it is not difficult to see that for a two-variable function with antisymmetry, the complete basis is the two-variable Slater determinant."

"Combined in a non-equilibrium strongly correlated system, atoms at high-energy sites replace low-energy sites and split into two Weyl nodes with opposite chirality through the Dirac cone, forming a multi-site effect. It has a non-equilibrium strong correlation state.”

"The above is the mathematical explanation of the non-equilibrium strongly correlated system, and it is also the content of my report today."

"Thank you all for listening patiently. I will organize the relevant content into corresponding papers in the future and publish it on the Arxiv preprint website for everyone to browse."

"Of course, if you have any questions, you can ask them now and I will do my best to answer them."

On the reporting table, as soon as Xu Chuan finished speaking, a prepared hand was raised from the audience.

It was Edward Witten.

Xu Chuan nodded, and his former mentor couldn't wait to speak: "In the strongly correlated electron system you reported, how is the entropy change of the non-equilibrium process defined?"

Hearing this question, Xu Chuan thought for a moment and looked around the report table out of habit, only to find that there was no chalk prepared on it.

Smiling, he looked at the staff under the reporting desk and said, "Can you please prepare two blackboards and a box of chalk for me?"

Upon hearing this, the staff member who was bored and in a daze because he could not understand the entire report process suddenly woke up, nodded quickly and trotted out.

After a while, several staff members rushed over dragging several blackboards.

Xu Chuan stepped forward, said thank you, took out a piece of chalk from the chalk box, and said while writing:

"A non-equilibrium system is a non-conservative, non-Hamiltonian system, so the entropy defined in a non-equilibrium system is not essentially equivalent to entropy in the thermodynamic sense."

"It can be defined by phase space contraction, that is, the phase space volume is not conservative for In contact with several mechanical systems Ci, σ(x)=∑jQj˙(x)/kBTj+R˙(x) can be derived according to the details I described before [1].

"., to sum up, R˙(x) is a term that can be eliminated in time averaging. Theoretically speaking, when I construct a non-equilibrium strong electron correlation system, σ(x) is the entropy change of the non-equilibrium system A definition.”

He stared closely at the blackboard that was projected on the podium after the screen was recorded. Looking at the calculations on it and listening to Xu Chuan's explanation, Edward Witten's eyes flashed with an inexplicable color.

When Xu Chuan finished speaking, he did not sit down, but continued to ask:

"So for the electron correlation system, the charge, spin and phase can form complex collective patterns under different nuclear configurations. How can you use your theory to explain it?"

Hearing this question, Xu Chuan shook his head involuntarily and replied:

"This question is beyond the scope of my answer. In the strongly correlated system, the electron Fermi system has a new strongly coupled collective behavior. Especially in the non-equilibrium state, the topology of the electron distribution phase or electron density distribution will lead to the Landau theory A new collective order outside the framework. I can’t find a more universal unified theoretical framework to answer your question.”

After a slight pause, he looked at Witten and continued: "However, in previous research, I have some understanding of this aspect, which may be able to answer some of your doubts."

As he spoke, he erased the calculations on the blackboard and wrote them again:

“Consider a typical strongly correlated system ‘one-dimensional transverse field Ising model’ whose Hamiltonian is: [H0=J(∑nL1σznσzn+1+ησzLσz1)h∑nσxn].”

"Among them, σxn^yn is the Pauli matrix; J>0 is the ferromagnetic interaction; >0 is the transverse field strength; L is the spin chain length; eta=1 represents the periodic boundary condition, and eta=0 represents the open boundary condition. "

"."

In front of the blackboard, Xu Chuan wrote on the blackboard his recent research on strongly correlated electronic systems.

Edward Witten's problem is also the goal he has been pursuing, to find a new framework and theory to unify various problems and theories in the strongly correlated electron system.

However, the strongly correlated electron system involves many cutting-edge fields of modern physics, such as condensed matter physics, atomic and molecular physics and quantum optics, quantum control and quantum computing, and non-equilibrium statistical physics.

The non-equilibrium quantum correlation phenomena that emerge in these different systems not only integrate the different characteristics of their respective systems, but also show universal general laws.

Its novelty and complexity make this type of system have a large number of unknown basic physical problems and novel physical phenomena. It is as difficult to find a new framework and theory to achieve unification as to solve one of the seven millennium problems.

Even if he was reborn and had a vision for the future, he could not find a suitable way to achieve this goal.

On the podium, while Xu Chuan was writing on the blackboard and explaining his research, he was also sorting out his ideas for studying the problems of the strongly correlated electron system.

Offstage, Edward Witten stared at the blackboard on the podium with a sharp gaze.

In the lecture hall, many mathematicians also focused their attention on the lecture table. Although most people could not understand what was written on the blackboards, and although the time had exceeded the originally expected half an hour, no one left.

Some people even took out their mobile phones and took videos to record.

On the lecture table, Xu Chuan was already immersed in his own world, sorting out his thoughts bit by bit.

It had been almost a week since he put down this research.

The original vague ideas reappeared in his mind at this time, and they were clearer and more natural.

[In the case of strong correlation, the spin-up operator is expressed by hand field as: ‘S+j(t)=eiθ(x, t)=eiθL(x+vt)iθR(xvt)’]

He wrote the last line of equations on the blackboard with chalk in his hand, and Xu Chuan breathed a sigh of relief. After all, this problem was not so easy to solve. He had been stuck here for a while.

He smiled, turned his head and looked at Edward Witten in the audience, and said:

"My research ends here. That is to say, in frequency space, by combining the Boltzmann function with the Monte Carlo method, the linear spectrum can describe the continuous spectrum of "spinons" with different momentum."

"And in this way, the explanation of multi-orbital correlation effect in non-equilibrium strongly correlated electron system can be completed, but how to spread this description to the entire strongly correlated electron system, I can't find a way yet."

"Maybe it has a solution, maybe it doesn't have a solution, at least now, the answer is probably only known by God who lives outside the dimensional space."

"Of course, I will continue in the next time."

Before he finished speaking, an idea suddenly flashed through his mind like a flash of inspiration.

"God? Dimensional space?"

The two key words flashed through his mind, and the unfinished words in his mouth were forcibly interrupted. Xu Chuan stood on the report table, his pupils radiating, and fell into deep thought.

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