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"Atomic interactions in everyday solids and liquids are so complex that some of these materials' properties continue to elude physicists' understanding. Solving the problems mathematically is beyond the capabilities of modern computers, so scientists at Princeton University have turned to an unusual branch of geometry
instead....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 every point. A hyperbolic plane is difficult to envision—the artist M.C. Escher used hyperbolic geometry in many of his mind-bending pieces—but is perfect for answering questions about particle interactions
The research team used superconducting circuits to create a lattice that functions as a hyperbolic space. When the researchers introduce photons into the lattice, they can answer a wide range of difficult questions by observing the photons' interactions in simulated hyperbolic space.
"You can throw particles together, turn on a very controlled amount of interaction between them, and see the complexity emerge," said Houck, who was the senior author of the paper published July 4 in the journal Nature.
"The problem is that if you want to study a very complicated quantum mechanical material, then that computer modeling is very difficult. We're trying to implement a model at the hardware level so that nature does the hard part of the computation for you," said Kollár.
"It's a space that you can mathematically write down, but it's very difficult to visualize because it's too big to fit in our space," explained Kollár."
Phys.Org
"Atomic interactions in everyday solids and liquids are so complex that some of these materials' properties continue to elude physicists' understanding. Solving the problems mathematically is beyond the capabilities of modern computers, so scientists at Princeton University have turned to an unusual branch of geometry
The research team used superconducting circuits to create a lattice that functions as a hyperbolic space. When the researchers introduce photons into the lattice, they can answer a wide range of difficult questions by observing the photons' interactions in simulated hyperbolic space.
"You can throw particles together, turn on a very controlled amount of interaction between them, and see the complexity emerge," said Houck, who was the senior author of the paper published July 4 in the journal Nature.
"The problem is that if you want to study a very complicated quantum mechanical material, then that computer modeling is very difficult. We're trying to implement a model at the hardware level so that nature does the hard part of the computation for you," said Kollár.
"It's a space that you can mathematically write down, but it's very difficult to visualize because it's too big to fit in our space," explained Kollár."
Phys.Org