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Posted on 07/27/2022 12:44:59 PM PDT by Red Badger
The researchers discovered that a new theoretical framework to unify Hermitian and non-Hermitian physics is established by the duality between non-Hermiticity and curved spaces.
A physics puzzle is resolved through a new duality.
According to traditional thinking, distorting a flat space by bending it or stretching it is necessary to create a curved space. A group of scientists at Purdue University has developed a new technique for making curved spaces that also provides the answer to a physics mystery. The team has developed a method using non-Hermiticity, which occurs in all systems coupled to environments, to build a hyperbolic surface and a number of other prototypical curved spaces without causing any physical distortions of physical systems.
“Our work may revolutionize the general public’s understanding of curvatures and distance,” says Qi Zhou, Professor of Physics and Astronomy.
“It has also answered long-standing questions in non-Hermitian quantum mechanics by bridging non-Hermitian physics and curved spaces. These two subjects were assumed to be completely disconnected. The extraordinary behaviors of non-Hermitian systems, which have puzzled physicists for decades, become no longer mysterious if we recognize that the space has been curved. In other words, non-Hermiticity and curved spaces are dual to each other, being the two sides of the same coin.”
Poincare Half Plane
A Poincaré half-plane can be viewed in the background which demonstrates a curved surface. The white geodesics of the curved surface are shown as an analog of straight lines on a flat space. White balls moving in the right direction demonstrate the geometric origin of an extraordinary skin effect in non-Hermitian physics. Credit: Chenwei Lv and Ren Zhang.
The team’s results were published in the journal Nature Communications in an article titled “Curving the Space by Non-Hermiticity.” Most of the team’s members are employed at Purdue University’s West Lafayette campus. The Purdue team is made up of Professor Qi Zhou, Zhengzheng Zhai, a postdoctoral researcher, with graduate student Chenwei Lv serving as the primary author. Professor Ren Zhang from Xi’an Jiaotong University, who is a co-first author of the paper, was a visiting scholar at Purdue when the study was originally started.
One must first comprehend the distinction between Hermitian and non-Hermitian systems in physics in order to comprehend how this discovery works. Zhou explains it using the example of a quantum particle that can “hop” between several locations on a lattice.
If the probability for a quantum particle to hop in the right direction is the same as the probability to hop in the left direction, then the Hamiltonian is Hermitian. If these two probabilities are different, the Hamiltonian is non-Hermitian. This is the reason that Chenwei and Ren Zhang have used arrows with different sizes and thicknesses to denote the hopping probabilities in opposite directions in their plot.
“Typical textbooks of quantum mechanics mainly focus on systems governed by Hamiltonians that are Hermitian,” says Lv.
“A quantum particle moving in a lattice needs to have an equal probability to tunnel along the left and right directions. Whereas Hermitian Hamiltonians are well-established frameworks for studying isolated systems, the couplings with the environment inevitably lead to dissipations in open systems, which may give rise to Hamiltonians that are no longer Hermitian. For instance, the tunneling amplitudes in a lattice are no longer equal in opposite directions, a phenomenon called nonreciprocal tunneling. In such non-Hermitian systems, familiar textbook results no longer apply and some may even look completely opposite to that of Hermitian systems. For instance, eigenstates of non-Hermitian systems are no longer orthogonal, in sharp contrast to what we learned in the first class of an undergraduate quantum mechanics course. These extraordinary behaviors of non-Hermitian systems have been intriguing physicists for decades, but many outstanding questions remain open.”
He further explains that their work provides an unprecedented explanation of fundamental non-Hermitian quantum phenomena. They found that a non-Hermitian Hamiltonian has curved the space where a quantum particle resides. For instance, a quantum particle in a lattice with nonreciprocal tunneling is in fact moving on a curved surface. The ratio of the tunneling amplitudes along one direction to that in the opposite direction controls how large the surface is curved.
In such curved spaces, all the strange non-Hermitian phenomena, some of which may even appear unphysical, immediately become natural. It is the finite curvature that requires orthonormal conditions distinct from their counterparts in flat spaces. As such, eigenstates would not appear orthogonal if we used the theoretical formula derived for flat spaces. It is also the finite curvature that gives rise to the extraordinary non-Hermitian skin effect that all eigenstates concentrate near one edge of the system.
“This research is of fundamental importance and its implications are two-fold,” says Zhang. “On the one hand, it establishes non-Hermiticity as a unique tool to simulate intriguing quantum systems in curved spaces,” he explains. “Most quantum systems available in laboratories are flat and it often requires significant efforts to access quantum systems in curved spaces. Our results show that non-Hermiticity offers experimentalists an extra knob to access and manipulate curved spaces.
An example is that a hyperbolic surface could be created and further be threaded by a magnetic field. This could allow experimentalists to explore the responses of quantum Hall states to finite curvatures, an outstanding question in condensed matter physics. On the other hand, the duality allows experimentalists to use curved spaces to explore non-Hermitian physics. For instance, our results provide experimentalists a new approach to access exceptional points using curved spaces and improve the precision of quantum sensors without resorting to dissipations.”
Now that the team has published their findings, they anticipate it spinning off into multiple directions for further study. Physicists studying curved spaces could implement their apparatuses to address challenging questions in non-Hermitian physics.
Also, physicists working on non-Hermitian systems could tailor dissipations to access non-trivial curved spaces that cannot be easily obtained by conventional means. The Zhou research group will continue to theoretically explore more connections between non-Hermitian physics and curved spaces. They also hope to help bridge the gap between these two physics subjects and bring these two different communities together with future research.
According to the team, Purdue University is uniquely qualified to foster this type of quantum research. Purdue has been growing strong in quantum information science at a fast pace over the past few years. The Purdue Quantum Science and Engineering Institute paired with the Department of Physics and Astronomy, allows the team to collaborate with many colleagues with diverse expertise and foster interdepartmental and collegiate growth on a variety of platforms that exhibit dissipations and nonreciprocal tunneling.
Reference: “Curving the space by non-Hermiticity” by Chenwei Lv, Ren Zhang, Zhengzheng Zhai, and Qi Zhou, 21 April 2022, Nature Communications.
DOI: 10.1038/s41467-022-29774-8
There was no ‘direction’, space just expanded rapidly.............
OR, we are living in a shadow cast by a higher spatial dimensional reality.
Easy, it all depends on your definitions of, "reason", "nothing" and "spring". I mean, after all, now that "recession" doesn't mean recession, why should those other words be a problem?
Miracles by definition rarely happen.
They are God’s way of telling you that your way of doing things needs to change.
You can’t get life from the tree of knowledge.
Miracles by definition rarely happen.
They are God's way of telling you that your way of doing things needs to change.
You can't get life from the tree of knowledge.
That's one amazing reply considering what I had been working on off of FR. I only popped in to grab the name of today's Top Gun thread title.
As I mentioned on the post 40 to which you replied, it's "All in the timing."
The dark side never learns because it already knows everything already.
Has it been demonstrated that the Eigenvalues are off by “more” if it’s a strong field (strong curvature), and by a lesser amount on a weak field (weak curvature)? If experimental results aren’t consistent with this then there’s still something wrong.
Both David & Solomon were great Kings and a terrible fathers. The sword never left David’s house after his affair with Bathsheba. His get of that tryst—Solomon in all his glory—the man who addressed so many excellent pieces of advice to his son in proverbs—in turn produced a twit in Rehoboam.
Perhaps both David and Solomon were motivated to write because they instinctively knew that their lives were off the mark. in the way that you and I know our lives are off the mark. (though we may have different markers.) In David and Solomon their mark may have been that instinctive sense of generations where great grand dad is followed by grand dad who is followed by dad who is followed by son who is followed grandson who is followed by great grandson. A man will know when he is in a proper continuation of his line. And when his actions are out line with that continuation.
nah, that’s probably too grandiose—or certainly too grandiose for the thinking of a young man—most of whom don’t think with their heads all that much anyway.
most conservatives today have experienced over the last many decades a sheering force on the foundations of the USA. Maybe that sheering force is what moved David and Solomon to write.
Musk could be the modern Noah. A guy — here at free republic someone wrote that the hebrew word for ark that noah used —and the hebrew word for basket that carried Moses as a baby on the nile—are the same word. Both baby and man were for a time completely in God’s hands...to do as He willed.
“The dark side never learns because it already knows everything already.”
The deep question is how do you open up the civilization to the ways of God.
So light comes in.
imho beyond you and I—(because all change has to start at home)—it has to start in the universities.
There needs to be a paradigm shift.
someone wrote that the hebrew word for ark that noah used -- and the hebrew word for basket that carried Moses as a baby on the nile -- are the same word.
"teva"
Definitions 5 and 7 loop back to my previous musical post (#40) about the letters in the spaces.
Also, acronym in Hebrew is "roshei teivot", lit. the heads of words (the word for word, "teva")
We know that the other famous Ark is the Ark of the Covenant: Aron ha-Brit.
... a sheering force on the foundations of the USA. Maybe that sheering force is what moved David and Solomon to write.
The acronym for the United States is [ארה״ב], which stands for the name of the US: Artzot ha-Brit, lit. lands of the covenant.
This common pattern for forming an acronym would generate the same "roshei teivot" for "Aron ha-Brit.
Of course, it's not like anyone's going to use that acronym for the Ark of the Covenant, otherwise people might see it and think that the Ark of the Covenant is the United States.
The deep question is how do you open up the civilization to the ways of God.
So light comes in.
>>>
There needs to be a paradigm shift.
US Government -- famous for its acronyms, and acronyms for acronyms. Who'd find anything in a US Government warehouse. It would be like finding a neil in a haystack.
You don't. It finds *you*.
An interesting point of debate in the Jewish spheres is whether the Messiah arrives and then the Temple is built, or if the Temple drops down, already built.
As you mentioned earlier...
Miracles by definition rarely happen.
They are God's way of telling you that your way of doing things needs to change.
An "Aha" light bulb moment is the sudden "miraculous" lightning speed arrival of an epiphany, not a material manifestation.
The miracle is the change required in order to see the light (revelation), because it's been sitting around all along.
"Say...what's a mountain goat doing way up here in a cloud bank?"
Behold, he cometh with clouds; and every eye shall see him...
GOAT! 5 Stars
Jordan Peterson does a good job in 17 minutes of explaining practical application of the Noah story.
https://www.youtube.com/watch?v=3dNGacak8Dc
about three weeks ago, the congress mandated that all the federal agencies bring to congress all the information they have since WWII on UFO’s.
this tucker carleson interview with stanford professor dr gary nolan—who is one of the foremost researchers in the world on UFO’s — was posted at freerepublic this morning. You’ll want to look at this in the evening —with company if you can arrange for that. Its an hour long.
https://freerepublic.com/focus/chat/4082867/posts?page=1
https://www.youtube.com/watch?v=u7cKhIJnTpo
I haven't seen any UFOs but rather some plain reality on the ground that is even more unbelievable, if you can believe it.
Here's a graphic I post every now and then because it sums it all up:
Dr. Nolan spoke of this being the type of something so big that it would cause people to unify.
Genesis 49
1.And Jacob called unto his sons, and said, Gather yourselves together, that I may tell you that which shall befall you in the last days.
2 Gather yourselves together, and hear, ye sons of Jacob; and hearken unto Israel your father.
Dr. Nolan spoke of this being the type of something so big that it would cause people to unify.
We’ve only seen 100 or so sci fi movies on this theme in last 50 years.
I don’t know that “space” itself is expanding...
Of course it is, you know why?
Because it’s trying to get away from Chuck Norris.
LOL, Good one! It sure says something about him that we are still calling him
“Mr. Tough Guy!”
Amazing what's been put out there through iconic movies, famous songs, world events and their celebrations and commemorations, popular quotes that become integrated into the common language, memes... it goes on.
Hello, Neil and Buzz. I'm talking to you by telephone from the Oval Room at the White House. And this certainly has to be the most historic telephone call ever made. I just can't tell you how proud we all are of what you've done. For every American, this has to be the proudest day of our lives. And for people all over the world, I am sure they too join with Americans in recognizing what an immense feat this is. Because of what you have done, the heavens have become a part of man's world. And as you talk to us from the Sea of Tranquility, it inspires us to redouble our efforts to bring peace and tranquility to Earth. For one priceless moment in the whole history of man, all the people on this Earth are truly one: one in their pride in what you have done, and one in our prayers that you will return safely to Earth.https://en.wikisource.org/wiki/Richard_Nixon%27s_Phone_Call_to_the_Moon
Can you give a three sentence max explanation of what hermiticity is—to the ordinary rubber necking gawker.
Then maybe a sentence or two more on why hermiticity is important, how fast the field progresses and what are its implications for the future?
Think of space as a 3d field- not empty.
The field is made of many layers of spandex, one on top of the other.
2 bb’s in the spandex are in same layers ( z) and 10 inches apart on the xy plane.
Now think of something (or many things) that pull the spandex, not the bb - between the bb’s- Creating a mound.
Now the bb are closer or further apart depending on whether they travel on the same spandex layer (further), or through spandex layers (closer).
This is analogous to changes in field density of space.
Or maybe not…
Your analogy is like the sun being at the bottom of a gravity well.
Just as earth is at the bottom of a gravity well?
The mass of both push down the fabric of space—so that things around them are pulled into them.
Correct?
So hermiticity measures the slope of the the gravity well?
I would say hermiticity measures the slope of the 3d field. Sorta…
the steeper the slope—the bigger the mass at the bottom of the gravity well?
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