New Physics-Inspired Proof Probes the Borders of Disorder
1 min read
Summary
In the 1950s, physicist Philip Anderson created a mathematical model to explain a strange behavior seen in some materials: When their atomic structure becomes sufficiently disordered, they suddenly insulate, impeding the flow of electrons.
Ever since, mathematicians have sought a rigorous proof that this transition occurs at a well-defined threshold.
That proof has proved elusive, but recent work has provided the first significant advances on the problem in decades.
The techniques they’ve developed could also be applied more broadly to other problems with similar structures.
In a series of papers, researchers have extended these techniques to describe systems with more dimensions, akin to the behaviors of electrons in our three-dimensional world.
With these new tools, mathematicians are hopeful that they’ll finally be able to prove the existence of the transition that first intrigued Anderson.
