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Strange geometry of distortion helps to cross scientific boundaries



  Strange Geometry of Distortion Helps Cross Scientific Borders
Princeton researchers have built an electronic array on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface in which space moves away from each point curves. Picture credits: Kollár et al.

Atomic interactions in everyday solids and liquids are so complex that some of the properties of these materials continue to elude physicists' understanding. The mathematical solution to the problems is beyond the capabilities of modern computers. Instead, Princeton University scientists have turned to an unusual branch of geometry.

Researchers led by Andrew Houck, a professor of electrical engineering, have built an electronic array on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface in which space curves away from itself at each point. A hyperbolic plane is hard to imagine ̵

1; the artist M.C. Escher used hyperbolic geometry in many of his insane works – but is perfect for answering questions about particle interactions and other challenging mathematical questions.

The research team used superconducting circuits to create a grid that acts as a hyperbolic space. By introducing photons into the lattice, researchers can answer a variety of difficult questions by observing the interactions of photons in simulated hyperbolic space.

and see the complexity emerge, "said Houck, who was the lead author of the paper, which was published on July 4 in the journal Nature .

Alicia Kollár, postdoctoral fellow at the Princeton Center for Complex Materials and According to the lead author of the study, researchers are expected to be able to answer complex questions about quantum interactions that determine the behavior of atomic and subatomic particles.

"The problem is that you want to study a very complicated quantum mechanical material, then this computer modeling is very difficult. We're trying to implement a hardware-level model for nature to do the hard part of the calculation for you, "said Kollár. [196] 59005] The centimeter-sized chip is etched with a circuit of superconducting resonators that move the microwave photon to motion and energy The resonators on the chip are arranged in a grid pattern of heptagons or seven-sided polygons.The structure is in a flat plane, but simulates the unusual geometry of a hyperbolic plane.

  Strange twist geometry helps to exceed scientific limits. </p><div><script async src=
  19659010] A schematic representation of the resonators on the microchip arranged in a grid pattern of heptagons or seven-sided polygons.The structure exists on a flat plane, but simulates the unusual geometry of a hyperbolic plane. Photo credits: Kollár et al.
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<p>  "There is no hyperbolic surface in normal 3D space," said Houck. "With this material, we can begin to think about mixing quantum mechanics and curved space in a laboratory environment." </p>
<p>  The attempt to force a three-dimensional sphere onto a two-dimensional plane shows that space is smaller on a spherical plane than on a plane. For this reason, the shapes of countries appear stretched when drawn on a flat map of the spherical earth. In contrast, a hyperbolic plane would have to be compressed to fit on a flat plane. </p>
<p>  "It's a space that you can write down mathematically, but it's very difficult to visualize because it's too big to fit in our space," Kollár explained. </p>
<p>  Regarding the effect of compressing hyperbolic space On a flat surface, the researchers used a special type of resonator, a coplanar waveguide resonator: when microwave photons pass through this resonator, they behave the same regardless of whether their path is straight or meandering.The meandering structure of the resonators provides the flexibility that is required Kollár said heptagons sides of the heptagons to create a flat tile pattern. </p>
<p>  The view of the chip's central heptagon looks like a fisheye camera lens, where objects at the edge of the field of vision appear smaller the farther they are from the center, the smaller the heptagons appear This allows microwave photons moving through the resonator circuit to behave like particles in a hyperbolic space. </p>
<p>  The ability of the chip to simulate a curved space could allow new investigations in quantum mechanics, including the properties of energy and matter in warped space-time around black holes. The material could also be useful for understanding complex relationships in mathematical graph theory and communication networks. Kollár noted that this research could eventually support the design of new materials. </p>
<p>  First, however, Kollár and her colleagues must further develop the photonic material by further investigating its mathematical foundations and introducing elements that allow photons in the cell to interact. </p>
<p>  "Microwave photons do not interact with each other – they happen directly," Kollár said. Most applications of the material would require "doing something so they can see that there is another photon there."
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Discovering natural material that shows hyperbolism in the plane


Further information:
Alicia J. Kollar et al., Hyperbolic Lattices in Circuit Quantum Electrodynamics, Nature (2019). DOI: 10.1038 / s41586-019-1348-3

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Princeton University




Quote :
Strange Distortion Geometry Helps Expand Scientific Borders (2019, July 12)
retrieved on July 12, 2019
from https://phys.org/news/2019-07-strange-warping-geometry-scientific-boundaries.html

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