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
Entity=century
What I know about distance is that it’s not a constant. The distance from my couch to the fridge to get a beer is inversely proportional to the amount of people in the house which also affects time.
The opposite is Greyhound Space, where a 4 hour trip takes 8 even though the bus is passing every car on the highway.
A whiter shade of pale.
Not if this is the explanation... ugh.
"We talking about the significance of the passage of time, right? The significance of the passage of time, so when you think about it there is great significance to the passage of time...There is such great significance to the passage of time when you think of a day in the life of our children.”So there you have it...don't take time too lightly.
If you see a woman in the distance you will notice that her spaces are curved.
As she approaches, her spaces become even more curved until it is total darkness coz it`s Saturday night.
And...
Go Boilers
I know Mitch Daniels doesn’t get any love on FR, but he’s certainly done good things at Purdue.
Here is a short excerpt which can lend assistance to FR readers of the current paper & thread...
"Topological edge states in topological materials are robust against weak perturbations, an ability originating from the global geometry of eigen wave functions in the Hilbert space1,2. Such an intrinsic geometric feature is captured by global topological invariants that are related to edge states through the bulk-boundary correspondence.
However, this conventional paradigm is challenged by localization under disorder3,4,5,6 or non-Hermiticity7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24, which have become the focus of study of late, particularly in light of recent experimental progress in synthetic topological systems25,26,27,28,29,30,31,32,33,34,35. On one hand, despite its gap-closing tendency, the disorder can induce topology from a trivial insulator. In the resulting topological Anderson insulator, the global topology emerges in a bulk with localized states, in the absence of translational symmetry3,4,5,6. On the other hand, in a broad class of non-Hermitian topological systems, the nominal bulk states are exponentially localized toward boundaries under the non-Hermitian skin effect8,9,10,11,12,13,14,15,16,17,18,19,20,21,22.
The deviation of the bulk-state wave functions from the extended Bloch waves invalidates the conventional bulk-boundary correspondence, necessitating the introduction of non-Bloch topological invariants8,9,10,11. While the two localization mechanisms differ in origin and manifestation, the topology of the underlying system gets fundamentally modified in either case.
Remarkably, in the recently proposed non-Hermitian topological Anderson insulator36,37,38,39, the two distinct localization mechanisms are pitted against each other, wherein the interplay of disorder, non-Hermiticity, and topology leads to exotic phenomena such as the non-monotonous localization, disorder-induced non-Bloch topological phase transitions, and biorthogonal critical behaviors.
In this work, we report the experimental observation of non-Hermitian topological Anderson insulators in single-photon quantum-walk dynamics. Driven by a non-unitary topological Floquet operator, the quantum walk undergoes polarization-dependent photon loss and acquires the non-Hermitian skin effect. In contrast to previously implemented quantum walks with the non-Hermitian skin effect30,35, our current experiment resorts to the time-multiplexed configuration, with the spatial degrees of freedom encoded in the discrete arrival time of photons at the detector40. This enables us to implement quantum walks with a larger number of time steps, which is pivotal for the current experiment. We introduce static random disorder through parameters of the optical elements41, which would result in a complete localization of bulk states in the large-disorder limit. In the intermediate regime with moderate loss and disorder, the competition between the non-Hermitian skin effect and Anderson localization yields non-monotonic localization features which we characterize by measuring the Lyapunov exponent20. Using the biorthogonal chiral displacement, we then probe the topological phase transition, which is in qualitatively agreement with theoretical predictions. At the measured topological phase boundary, the biorthogonal localization length diverges, consistent with the biorthogonal critical nature of the phase transition36,37,38. We further measure topological edge states from dynamics close to the boundary of the non-Hermitian topological Anderson insulator."
By: Quan Lin, Tianyu Li, Lei Xiao, Kunkun Wang, Wei Yi & Peng Xue
Nature Communications has hundreds of similarly interesting articles...
This sounds like word speak like AOC would use except too big of words.
me thinks the intent of the article is stating ALL space is curved... but we already knew that. 2D (straight line/point) dimension isn’t our human experience. They are ‘looking’ beyond 3D within particle physics/quanta, trying to map/explain/formulate.
This is my interpretation of it (not understanding Hamiltonians or Hermitian spaces at all):
If a particle is being acted on by some external force that gives it a preference in the direction of travel (for example, gravity making it easier to move down than up, or an electric or magnetic field having the same kind of effect), then we can model that preference as a curved space instead of a flat space. In this case, it is easier for the particle to move ‘down’ the curve instead of ‘up’ the curve.
Therefore, the quantum properties that should be orthogonal but aren’t due to the external force, actually turn out to be orthogonal to the curved surface, just like gravity is always pointing to the center of the earth and the direction changes as you move along the earth’s surface. This happens with gravitational force on a ramp, as well. Gravity makes a ball roll down the ramp because a portion of the gravitational force is down the ramp (and the other part is toward the ramp surface), whereas if the ramp were flat, it all points down toward the center of the earth and there is no motion.
So, the properties are orthogonal to this curved surface and are not orthogonal to the flat surface and this fact can now be used to make better equations that model the behavior. It seems to be just a better way of modeling the behavior of the system.
I think you are hitting on the guts of it.
If we look at time, distance, space, energy, matter etc. naturalistically, then we are simply agonizing over our ability to observe, deduce, interpolate but not really getting to the heart of the matter.
Nothing happens without input, action, energy intent etc, iows, an actor, a prime cause. To think otherwise is lunacy (a space term!).
So, if we simply assume everything has a purpose, was purposeful and thought out, then we really ought to be looking not at the “stuff” or it’s mechanisms, but rather to the Creator. These days the naturalistic is god. It is not. It is simply our attempt to define without attribution.
God is. Everything else is his creativity.
Who dares look at all of these issues through that lens? We all get the same facts, what do we do with them?
Space time energy matter, created by a Creator. Must be a reason.
We have long separated the philosophic from the rational to our lack I think.
I will look to the author, so I can understand his words. Many will look at the words and deny an author...
“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.”
Oh good. They have discovered the cause of Hemorrhoids. Oh wait .... wrong article.
That's a copout. The question exists and can't be answered. Saying it is a theological question avoids embarrassment.
Would you have liked my initial response better if I said “metaphysics\philosophy” rather than “theology”? On this subject they’re almost interchangeable. I don’t understand the point of your somewhat hostile response. Actually, any question can be asked whether it can be asked intelligently is the issue. Right now, physics has no meaningful or intelligent way to ask that question. The physics and math to express it don’t exist yet. That was my point!
I wrote poetry when I was in my 20’s as an antidote to my political science major. Poly sci taught Students how to use roughly 1000 words where roughly 10 words would do.
Poly sci at the time was not a real major. So it taught students how to be baffling. The saying was if you can’t dazzle them with your brilliance. Baffle them with your BS. Poly sci major’s learned to be bafflers.
That major wasted me. Baffle others and you baffle yourself.
That’s why speaking the truth with simplicity helps both the speaker and the listener.
To this day when I’m way out beyond my ken — I still resort to poetry. A good rhyme heals the spaces between what I think I know, what I know I don’t know and what I don’t know that I don’t know. That’s sec def speech. But concise as I can get for the atheist.
Who shall I say has sent me? (Tell them—I am who I am has sent you.) That’s both true and a play on words—not to mention OT humor)
Thank you for noticing.
A good rhyme heals the spaces between what I think I know, what I know I don't know and what I don't know that I don't know.
Space rhymes with
Between my own hodgepodge of understanding and web translators, I saw on the Hebrew Wikipedia page for the musical staff (called "chamsha" for the five lines), that:
"the space between the lines is called 'beinah'"
בינה
Essentially a noun for "between", but spelled the same as binah, "understanding." To quote from a page I've had open in the background for most of the day:
The root of Bina creates the word "Bein" which means: "between [in the sense of comparison]".
https://www.13petals.org/bird/
(To this day when I'm way out beyond my ken)
Who shall I say has sent me? (Tell them -- I am who I am has sent you.) That's both true and a play on words -- not to mention OT humor)
Seen this page?
There's that same oddly placed proverb that's not exactly a proverb. It's a simple, wise saying that also stands out because it is not formatted like the others, so I had taken a closer look:
It begins with a bullet (all others are line indents), which is ALT 7 which is Unicode 2022.
(7/2022)
All in the timing. There's way more to the saga, but briefly -- when I "initially" followed the edit trail upon finding it on March 9th, it led to a sign in the middle of nowhere that signalled the Exodus. Pretty obvious imagery for anyone willing to.. read between the lines. I can describe further if you so request.
Why say in 15, what you can say in 10? 😉
For those who like to play.
Great sign-up date, by the way.
In the future, it wasn't like anyone was going to steal the body.
Physics Mystery Solved: Findings Could “Revolutionize” Our Understanding of Distance
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