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
Can someone explain in some easy way.
For example, I think that everyone gets that the universe is expanding because space itself is expanding. No one quite knows how space itself can expand but ok so space is expanding.
Further, gravity bends space so light curves when it goes around dense stars and even black holes.
So can someone connect those two observations with the math and observations of this article?
The Sandworms can have the spice, but what I learned was that hermits have their own physics!
Ping!...................
Just tell me what is on the other side of nothing. Does nothing never end?
But only God knows, because he’s already there.
“ Just tell me what is on the other side of nothing”
The official platform of the entrenched RNC
I wish I could........................
Yikes......that article went so far over my head, it almost knocked the Webb telescope out of orbit.......
Can someone explain in some easy way.
For example, I think that everyone gets that the universe
is expanding because space itself is expanding.
No one quite knows how space itself can expand
but ok so space is expanding.
Further, gravity bends space so light curves
when it goes around dense stars and even black holes.
So can someone connect those two observations
with the math and observations of this article?
It's like something out of a Robert Frost poem.
(I've been watching too much Gutfeld.)
That’s theology. Physically (meaning using current physics!) the question can’t be asked.
I don’t know that “space” itself is expanding, but everything inside of it is.
I’m hoping that the Webb telescope will show us what’s really “out there” in the manner that the two radio astronomers discovered the cosmic background radiation, only in a visual sense.
I have a difficult time when I’m confronted with higher forms of physics.
E=mc squared I get. I have a hard time with quantum physics and the like.
Not that I don’t believe in it, I get a headache trying to understand it.
I really don’t give a flying fig. I know how far away the grocery store, gym, and my daughter’s house are. The rest of space can expand or shrink all it wants. BFD.
How’s that for a scientific explanation?
From what I read there, it seems that previous assumptions of the relationships of particles (presumed to be on a “flat space”) were giving wonky answers when trying to figure how they moved. By using a different notation describing a curved space then observations “worked out” better.
But I’m probably seriously misguided ;-)
There being no duality...pluralism is untrue...
Meditate on compassion.
A remedial question before answering how to fold space without physical distortion…when the Big Bang occurred did it shoot matter primarily in one direction or did it shoot in all directions?
“The hard swallow built into science is this business about the big bang…
This is the notion that the universe, for no reason, sprang from nothing in a single instant… notice that this is the limit test for credulity.
Whether you believe this or not, notice that it is not possible to conceive of something more unlikely, or less likely to be believed.
I defy anyone. It’s just the limit case for unlikelihood: that the universe would spring from nothing in a single instant for no reason… ”
-Terence McKenna
I would say all directions instantaneously within a planck time it was done. This was complete with far distant galaxies light reaching us instantaneously (when it should have taken millennium). And on top of all of that, we are living in a computer simulation.
Damn, it is about time. I am tired of struggling with the subtle nuances of time and space.
My dad, long gone now, told me as a young boy looking at stars in the cold clear central NY winter, probably around 1973 or so, when I asked him how far were the stars? His response was classic. “Son, they are just always a bit farther than you can reach”.
He was right. Most of what we know of space and distance and time are turning out to be rather simplistic and archaic, even though only a entity old....
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