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 coefficient bi(x1) can be obtained as a function of the first variable."
"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 stage, as soon as Xu Chuan finished speaking, a prepared palm was raised from the audience.
It's 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?"
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:
"The non-equilibrium system is a non-conservative non-Hamiltonian system, so the entropy defined in the non-equilibrium system is not essentially equivalent to the entropy in the thermodynamic sense."
"It can be defined by phase space contraction, that is, the phase space volume is not conservative for
System C0 is in contact with several mechanical systems Ci, and we can derive σ(x)=∑jQj˙(x)/kBTj R˙(x) 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, in my construction of a non-equilibrium strong electron correlation system, σ(x) is the non-equilibrium
A definition of the entropy change of the system."
He stared closely at the blackboard that was recorded and projected on the podium, 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 should 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 cannot 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, and I may be able to answer some of your doubts."
As he spoke, he erased the equation on the blackboard and wrote it again:
“Consider a typical strongly correlated system ‘one-dimensional transverse field Ising model’ whose Hamiltonian is: [H0=?J(∑nL?1σznσzn 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 strongly correlated electronic systems.
However, strongly correlated electronic systems involve condensed matter physics, atomic and molecular physics and quantum optics, quantum control and quantum computing, non-equilibrium statistical physics and many other frontier fields of modern physics.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! The non-equilibrium quantum correlation phenomena emerging in these different systems not only integrate the different characteristics of their respective systems, but also show universal general laws.
Its novelty and complexity result in a large number of unknown basic physical problems and novel physical phenomena in this type of system. It is no less difficult to find a new framework and theory to unify it than to solve it.
One of the Seven Millennium Problems.
Even if he was reborn and had a vision for the future, he still couldn't find a suitable way to accomplish 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 difficult problems of strong electron correlation systems.
Under the stage, Edward Witten stared at the blackboard on the reporting table with blazing eyes.
In the lecture hall, many mathematicians also focused their attention on the lecture table. Although most of them could not understand what was written on the blackboards, and even though the time had exceeded the originally expected half hour, they still
No one left.
Some people have even started to take out their mobile phones and take videos and record them.
On the reporting stage, Xu Chuan was already immersed in his own world, sorting out the thoughts in his mind bit by bit.
It has been almost a week since he put down this research.
Ideas that were already somewhat fuzzy will resurface in your mind, becoming clearer and more natural.
[In the case of strong correlation, the spin promotion operator is expressed as a chiral field: 'S j(t)=e?iθ(x,t)=e?iθL(x vt)?iθR(x?vt)
'】
The chalk in his hand listed the last line of calculations on the blackboard. Xu Chuan breathed a long sigh of relief. After all, this problem was not so easy to solve. He had been stuck here for some time.
He smiled, turned to look at Edward Witten in the audience, and said:
"My research ends here, that is to say, in frequency space, through the combination of Boltzmann function and Monte Carlo method, linear spectrum can describe the continuous spectrum of "spinons" with different momentum.
"
"In this way, the explanation of the multi-orbital correlation effect in the non-equilibrium strongly correlated electron system can be completed, but I still can't find a way to extend this description to the entire strongly correlated electron system."
"Maybe it has a solution, maybe it doesn't have a solution. At least for now, I'm afraid only God who lives outside the dimensional space knows the answer."
"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? Dimension space?"
Two key words flashed through his mind, and the unfinished words in his mouth were forcibly interrupted. Xu Chuan stood on the reporting table, his pupils shining, and he was lost in thought.
........
PS: Today’s update is 8,000 words, please vote for me!
