In the 1950s, Philip Anderson, a physicist at Bell Laboratories, discovered a strange phenomenon. In some situations where it seems as though waves should advance freely, they just stop — like a tsunami halting in the middle of the ocean.
Anderson won the 1977 Nobel Prize in physics for his discovery of what is now called Anderson localization, a term that refers to waves that stay in some “local” region rather than propagating the way you’d expect. He studied the phenomenon in the context of electrons moving through impure materials (electrons behave as both particles and waves), but under certain circumstances it can happen with other types of waves as well.
Even after Anderson’s discovery, much about localization remained mysterious. Although researchers were able to prove that localization does indeed occur, they had a very limited ability to predict when and where it might happen. It was as if you were standing on one side of a room, expecting a sound wave to reach your ear, but it never did. Even if, after Anderson, you knew that the reason it didn’t was that it had localized somewhere on its way, you’d still like to figure out exactly where it had gone. And for decades, that’s what mathematicians and physicists struggled to explain.
This is where Svitlana Mayboroda comes in. Mayboroda, 36, is a mathematician at the University of Minnesota. Five years ago, she began to untangle the long-standing puzzle of localization. She came up with a mathematical formula called the “landscape function” that predicts exactly where waves will localize and what form they’ll take when they do.
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