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 t
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.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 athas developed a new technique for making curved spaces that also provides the answer to a physics mystery.
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.in an article titled “Curving the Space by Non-Hermiticity.
“Typical textbooks of quantum mechanics mainly focus on systems governed by Hamiltonians that are Hermitian,” says Lv. 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.
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.
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