A genius? I just love studying.

Chapter 156 Fractal Structures, Models, and the Dawn of a New Era
“Inelastic neutron scattering test on G-17”.

After a moment of calculation, Chen Hui looked up again.

This time, however, no one moved.

The so-called inelastic neutron scattering test is an important experimental technique for studying the microscopic dynamic properties of materials by utilizing the interaction between neutrons and matter. It obtains dynamic information about atoms or magnetic moments inside the material, such as lattice vibrations, spin fluctuations, and molecular motion, by measuring the energy and momentum changes when a neutron collides with a sample inelastically.

This is different from the previous electron microscopy scans. This experiment is simply beyond the capabilities of their laboratory. They don't even have the equipment needed for neutron source preparation. Not to mention their laboratory, the entire Jiangcheng University doesn't have any.

It requires borrowing equipment from research institutes such as the China Institute of Atomic Energy or the China Spallation Neutron Source, as well as a large number of control and detection devices.

Such experiments are obviously very expensive. International neutron sources, such as J-PARC in the island nation and ISIS in Europe, charge about 3 to 10 yuan per hour. China's own neutron source is much cheaper, costing only 5000 to 20000 yuan per hour.

However, a single inelastic neutron scattering test can take at least several hours, or even several days.

They've been working on this project for over a year, but they've only done one inelastic neutron scattering test.

To conduct such an expensive experiment on a piece of scrap material now is something that even Xiao Meng, let alone them, couldn't make the decision on.

Everyone looked at Xiao Meng and Guo Senlin as they entered the laboratory.

"Ghost Shadow Peak, is it possible that it's just a measurement error?"

Guo Senlin felt a jolt of fear under those gazes and quickly spoke.

Good heavens, this isn't an experiment, this is just burning money!

I knew he would never have come here.

Xiao Meng was also caught in a dilemma. Not to mention that she didn't have the funds right now, even if she did have enough, she would hesitate to do such a test on a piece of scrap.

Seeing everyone's reaction, Chen Hui understood. He also had a Level 3 physics certificate, so he naturally knew that such an experiment was not cheap.

But that's not important. He wanted to test it simply to verify his findings and get a more accurate answer.

Even without this experiment, he could still make inferences based on the existing information.

These irregular holes are not defects at all, but a special fractal structure!

Chen Hui left his seat, went to the whiteboard, picked up a marker, pondered for a moment, and then quickly wrote a series of formulas on the whiteboard.
ξ=πv/Δω√(D/2D)
Where ξ represents the localization length, Δω is the phonon spectral linewidth, and D is the fractal dimension.

This formula is not difficult for people in the laboratory to understand. Yang Chi immediately picked up the paper and pen next to him, plugged in the experimental data, and calculated that when v=3200m/s and Δω=0.05THz, ξ≈5.2nm, which is surprisingly consistent with the average spacing of the holes observed by the electron microscope (5.0±0.3 nm)!
This means that fractal structures create perfect localization traps!

But that wasn't all. After final verification, Chen Hui finally perfected the model in his mind, and his marker flew across the whiteboard, writing formula after formula.

The hole structure is quantized using the Hausdorff dimension D, and a fractional integral is introduced to characterize the phonon path. Phonon scattering is then reconstructed, and the traditional scattering probability is replaced by the Riesz potential function to describe the interaction between phonons and fractal defects. Finally, the influence of the fractal field on the energy band is calculated using a non-equilibrium Green's function.

A new model has clearly emerged!

By inputting the experimental data into the model, it was found that this so-called defect, namely the fractal structure discovered by Chen Hui, induces flat bands, which significantly enhance the Seebeck coefficient.

"Using a helium ion microscope to artificially carve golden ratio fractal holes on a normal CuSe thin film!"

Xiao Meng immediately realized the significance of this discovery. Ignoring the fact that Dean Guo was right next to her, she put on her lab coat and personally began to operate the device.

This experiment was also challenging, but fortunately, all the necessary instruments were available in the laboratory.

When Xiao Meng finished carving and brought the thumb-sized CuSe film to the in-situ electron microscope, her usually steady hands couldn't help but tremble slightly.

"Low-frequency phonons (<1 THz) propagate spirally along the boundary of the fractal hole, and after undergoing 7 reflections (Fibonacci sequence), their energy decays to zero!"

Deng Ting stared at the testing equipment and said in a trembling voice.

After obtaining stable data, Xiao Meng continued operating the instrument.

High-frequency phonons (>3 THz) are directly captured by the golden ratio apertures, forming a stable standing wave mode. When the electron beam passes through the aperture network, it shows quantum interference fringes—proving that the fractal structure induces coherent enhancement of the electron wave function!

They succeeded!
"What we perceive as a flaw... is actually the optimal solution for natural writing!"

Xiao Meng looked at the final experimental results and muttered to himself.

Who would have thought that the final success would come from a piece of experimental waste that they had abandoned for three months?

She looked again at the little boy with the tender face next to her.

This person not only constructed a completely new model, but also easily discovered this amazing fractal structure, both of which were significant discoveries even for her.

Verification of the fractal structure is only the first step. Although it is already 9 p.m., no one has stopped working.

By modifying molecular beam epitaxy equipment and using stochastic differential equations to control the deposition rate, copper selenide films filled with fractal pores were grown on germanium substrates...

Everyone began preparing sample number 34 in an orderly manner.

"Temperature gradient test begins."

Xiao Meng started the laser flare machine.

The data screen flickered, and Deng Ting's eyes were bloodshot, but she stared intently at the testing equipment, not missing a single subtle sign.

"The thermal diffusivity is 0.32 mm/s, and the theoretical thermal conductivity is 0.89 W/m·K!"

"60% lower than the existing record!"

Deng Ting exclaimed in surprise.

But then, the Seebeck coefficient monitor suddenly sounded an alarm—the value was plummeting.

“The charge carriers have been captured by the fractal interface…” Chen Hui quickly recalculated the energy band. “Immediately inject argon plasma and use ion bombardment to open the quantum tunneling channel!”

Time passed slowly, and everyone was immersed in the intense preparation work.

Ten hours later, the final sample was finally formed.

Amidst everyone's eager gaze, it was sent into the integrated testing chamber.

“塞贝克系数420μV/K，电导率1.8×10^5 S/m，热导率1.05 W/m·K……”

Deng Ting's voice trembled, "At 723K, the ZT value reached 2.1!"

Yang Chi stared blankly at the screen, "This...this exceeds the requirements of NASA's deep space probes..."

Chen Hui, however, stared at the morning light outside the window. "No, this is just the beginning. If we introduce hyperbolic metamaterials as phonon filters, combined with my stochastic resonant doping model..."

Xiao Meng slammed his coffee cup down on the table. "Stop! Write your paper first!"

“Both the model and the fractal structure can be published as separate papers. Chen Hui is the first author. Does everyone agree?” Xiao Meng glanced around the lab and looked at the group, who looked tired but were in high spirits. “Yang Chi is the first author of the paper on the exploration of new thermoelectric materials.”

"Deng Ting, you write the patents for fractal structures and novel thermoelectric materials."

"Chen Hui, you can write your paper first, but don't rush to publish it. Wait until the patent is approved before submitting it."

Chaumont specifically gave him a word of advice.

The results of mathematical research are undoubtedly papers, but physics research can generate economic benefits. For many university-industry collaborative projects, corporate investors even focus only on the output of patents and not on papers.

This is also a good thing. In the past, China did not pay attention to patents, which resulted in many of its own inventions being patented by others, leaving it vulnerable to external control.

For example, Tu Youyou, the discoverer of artemisinin, has the achievement, but the patent was taken by Novartis in Switzerland, which has instead created a patent barrier for us.

Although she won the Nobel Prize decades later for this research, she had nothing to do with the results. At the time, many departments had the relevant technical materials and were vying to cooperate with foreign companies, but she was the only one excluded.

She only received a second-class invention award from the Chinese government, with a prize of 500 yuan, but she only received 200 yuan.

Having learned such a painful lesson, Chinese researchers now place much greater emphasis on patents.

As for Xiao Meng's allocation, no one had any objections, nor could they possibly have any. It's only natural that those who are capable should do more work and those who do more should receive more.

After doing all this, Xiao Meng finally came to Guo Senlin's side.

The old man had stayed up all night with them yesterday, and his complexion wasn't very good. Even the slight blush on his cheeks from excitement made Xiao Meng sense a dangerous aura.

"The college still has two million in discretionary funds; I'll approve them for you as soon as I get back."

Guo Senlin said excitedly that he was very glad that he had come in person and was able to become a witness to this history.

Although he is now focused on administration, he was a physics student in his day and still keeps up with the latest developments in physics. He naturally understands the importance of Xiao Meng and his team's breakthrough. This is not only a groundbreaking advancement in condensed matter physics, but it will also have a huge impact on the global landscape.

Of course, it has an effect that is infinitely beneficial to China!

"If that's not enough, I'll organize another review meeting. Please increase the funding for your new research project; let's tentatively set it at 50 million!"

He added.

"clear."

Xiao Meng smiled and said, "But you should go back and rest first. I'll see you off."

She was really worried that the old man would suddenly collapse to the ground; that would be a real problem.

As they walked out of the lab, Guo Senlin suddenly asked, "Is that little guy your new graduate student?"

Xiao Meng shook his head with a look of regret, "He's not my student, he's Yuan Xinyi's student, and he's not a graduate student, he's a freshman!"

"It's said that he got a perfect score on the IMO gold medal and was admitted to the university without taking the entrance exam before even finishing his first year of high school."

"What? Our Jiangcheng University can recruit an IMO gold medalist?"

Guo Senlin stared in astonishment.

Moreover, the abilities that little guy displayed were far beyond what a gold medal could describe.

How can such a talented person stay in the School of Mathematics? He should come to the School of Physics!

But that old fellow Wang Qiming is not someone who can be easily fooled.

Guo Senlin remained silent the entire way, but his mind was racing with thoughts.

……

At Duke University, in the editorial office of the Duke Mathematics Journal, Dobessi stared at his email inwardly, annoyed.

Double-blind peer review is the standard procedure for Duke Mathematics journal when accepting papers. If a paper is of very high caliber, it may be reviewed by multiple people, and it is even possible to hold a presentation for the paper.

Of course, this paper is interesting, but it doesn't quite meet that standard.

Another academic editor has already provided their review comments, but Bryant remains silent.

She had already reminded Bryant two weeks ago that she should have changed the academic editor for the paper if she hadn't received a positive response.

damn it!
Dobess cursed under his breath and, belatedly, assigned the paper to another professor at MIT.

Meanwhile, the Mathematics Department administration building,
"Hey, Spinger, I think you'll be interested in this paper!"

Bryant sat in his office, phone in hand, and laughed heartily as he spoke.

On the other end of the phone was Spengler, editor of *Mathematical Physics Communications*, and also a highly accomplished mathematical physicist who has long served at the Perimeter Institute for Theoretical Physics in Canada, leading interdisciplinary research in quantum systems and statistical mechanics. He also serves as a researcher at the Max Planck Institute for Mathematical Research, promoting the application of operator theory and spectral analysis in mathematical physics.

Under his pressure, Oliver finally abandoned his last bit of restraint and directly used the conclusions of that paper to publish his own.

Clearly, they chose the potential from "Mathematical Physics Communications".

Duke Mathematics was originally their best choice, their main platform, but unfortunately, that bitch Dobesie isn't stupid. Submitting his paper there was a real possibility of its fate.

Although *Mathematical Physics Communications* is theoretically a double-blind peer reviewer, given Bryant's extensive network over the years, he could easily identify the academic editor of the paper after submission, as there are only a handful of top scholars in this specific field.

He certainly wouldn't rush the other party to get the manuscript approved, but he would remind them that the paper was very interesting and could be accepted.

"You've taken on a good student!"

While on the phone, Spinger read the paper, "Applications of the Langlands Program in Condensed Matter Physics." Just reading the title and abstract piqued his interest.

He has been committed to promoting the interdisciplinary application of mathematics, which is undoubtedly a good practice.

He happened to have some free time. If it weren't for Bryant's call, he might have chosen to walk his cats and dogs and take a good rest. But since Bryant had called, he didn't mind checking out the rising stars in academia.

When Oliver finished writing his paper, it had already been uploaded to arXiv, so there was no need for double-blinding. Springer naturally knew who the author of the paper under his supervision was.

Many journals do not accept papers published on pre-publishing platforms, but Mathematical Physics Communications does not have this requirement. As long as your paper is of good quality, it can be published.

"I'll take a good look at it. If there are no problems, it will appear in the next issue of Mathematical Physics Communications."

Springer knew why Bryant was calling; he had heard that Bryant was working hard for a major opportunity, and he figured the publication of this paper would give him some help.

"Praise be to you, generous Spenger!"

Bryant laughed and hung up the phone, then dialed another academic editor's number.

(End of this chapter)