New duality solves a physics puzzle

New duality solves a physics puzzle

Poincaré’s semi-plane can be seen in the background, showing a curved surface. The white geodesy of a curved surface appears as an analogue of straight lines on a flat area. White balls moving in the right direction show the geometric origin of the extraordinary skin effect in non-hermetic physics. Credit: Chenwei Lv and Ren Zhang.

In conventional wisdom, the production of a curved space requires deformations, such as the bending or extension of a flat area. A team of Purdue University researchers has discovered a new way to create curved voids that also solves a physics puzzle. Without any physical distortions to the physical systems, the team designed a diagram using non-hermiticity, which is found in any systems paired with environments, to create a hyperbolic surface and a variety of other typical curved spaces.

“Our work may revolutionize the general public’s understanding of curvatures and distances,” says Qi Zhou, a professor of physics and astronomy. “It has also answered longstanding questions in non-Hermitian quantum mechanics by bridging the gap between Physics and curved distances. These two topics were supposed to be completely separate. The unusual behavior of non-hierarchical systems, which has puzzled physicists for decades, is no longer a mystery if we realize that space was curved. In other words, the non-straight and curved spaces are double with each other, being two sides of the same coin.

The team recently published their findings in Nature Communications. Most of the team members work on Purdue University’s West Lafayette campus. Chenwei Lv, a graduate student, is the lead author, and members of the Purdue team include Professor Qi Zhou, and Zhengzheng Zhai, a postdoctoral fellow. Co-first author, Professor Ren Zhang of Xi’an Jiaotong University, was a visiting researcher at Purdue when the project began.

In order to understand how this discovery works, one must first understand the difference between hierarchical and non-hierarchical systems in physics. Zhou explains it using an example in which a quantum particle can “jump” between different locations on a network. If the probability of a quantum particle jumping in the right direction is the same as the probability of jumping in the left direction, then the Hamiltonian is Hermetic. If these two possibilities are different, then the Hamiltonian is not a Hermetic. This is why Chenwei and Ren Zhang used arrows of different sizes and thicknesses to indicate the possibilities of moving in opposite directions in their chart.

“Model quantum mechanics textbooks focus mainly on systems governed by hierarchical Hamiltonians,” says Lv. “A quantum particle moving in a network needs equal probability to tunnel along the right and left directions. While Hamiltonians are well-established frameworks for studying isolated systems, coupling processes with the environment inevitably lead to dissipation in open systems, which may give rise to Hamiltonians no longer For example, the amplitude of the tunnel in the network is no longer equal in opposite directions, a phenomenon called non-reciprocal tunneling. In such non-hierarchical systems, the results of familiar textbooks no longer apply and may even appear to be completely opposite to Hermitian systems. For example, The eigenstates of non-Hermitian systems are no longer orthogonal, in sharp contrast to what we learned in the first semester of an undergraduate quantum mechanics course. These unusual behaviors of non-Hermitian systems have gripped physicists for decades, but many outstanding questions remain.”

He further shows that their work offers an unprecedented explanation for fundamental, non-hierarchical quantum phenomena. They find that a non-Hermitian Hamiltonian is curved outer space Where is the quantum particle located. For example, a quantum particles In a network with a non-reciprocal tunnel that actually moves on a curved surface. The ratio of the tunnel amplitude along one direction to the opposite direction controls how much the surface is curved. In such curved spaces all non-hierarchical peculiar phenomena, some of which may seem immaterial, immediately become normal. It is finite curvature that requires perpendicular conditions distinct from those of flat surfaces. As such, orthogonal eigenstates will not appear if we use the derived theoretical formula for flat areas. It is also the finite curvature that leads to the exceptional non-hierarchical skin effect in which all eigenstates are concentrated near one edge of the system.

“This research is of fundamental importance and its implications are twofold,” Zhang says. “On the one hand, it establishes non-erosion as a unique tool for simulating intriguing quantum systems in curved spaces,” he explains. “Most quantum systems available in laboratories are flat and often require significant efforts to access quantum systems in curved spaces. Our results show that non-striation provides experimentation with an additional handle for accessing and manipulating curved spaces. An example of this is that a hyperbolic surface can be created and attached further by Magnetic field This could allow the experiment to explore the responses of quantum Hall states to finite bends, a prominent question in condensed matter physics. On the other hand, dualism allows experiments to use curved spaces to explore non-hierarchical physics. For example, our results provide specialists with a new approach to access Exceptional points by using curved distances and improving the accuracy of quantum sensors without resorting to dissipation.”

Now that the team has published their findings, they expect it to spin in multiple directions for further study. Physicists who study curved spaces can use their devices to tackle challenging questions in non-hierarchical physics. Also, physicists working on non-hierarchical systems can model the dissipation to reach non-trivial curvilinear spaces that are not easily obtainable by conventional means. Zhou’s research group will continue to explore more connections between non-hierarchical physics and theoretically curved spaces. They also hope to help bridge the gap between these two physics topics and bring these two different communities together in future research.


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more information:
Chenwei Lv et al, Curving Space by Non-Hermiticity, Nature Communications (2022). DOI: 10.1038 / s41467-022-29774-8

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