Physical Address
304 North Cardinal St.
Dorchester Center, MA 02124
But in some ways, the evidence was somewhat unsatisfying. Zhitomirskaya and Avila used a method that is only applicable for some irrational values of alpha. By combining this with an intermediate proof that came before, they can say the problem is solved. But this collective evidence was not elegant. It was a patchwork quilt, each square stitched with individual logic.
Moreover, the evidence only confirmed the hypothesis that was originally stated, which involved making simplified assumptions about the electron’s environment. A more realistic situation is messier: the atoms in the solid are arranged in more complex patterns and the magnetic fields are not perfectly constant. “You’ve verified it for this one model, but what does it have to do with reality?” said Simon BakerA mathematician at the Swiss Federal Institute of Technology Zurich.
In this more realistic scenario you need to change the part of the Schrödinger equation where alpha appears. And when you do, the 10-martini proof stops working. “It was always annoying to me,” Zhytomirskaya said.
Breaking the proof into this larger context also implies that the beautiful fractal patterns that emerged—Cantor sets, Hofstadter’s butterflies—were nothing more than a mathematical curiosity, something that would disappear once the equation became more realistic.
Avila and Zhitomirskaya moved on to other problems. Even Hofstadter had doubts. If an experiment ever found her butterflies, she would write Gödel, Escher, Bach“I’ll be the most surprised person in the world.”
But in 2013, a group of physicists at Columbia University Dr In a lab his butterfly is imprisoned. They placed two thin layers of graphene in a magnetic field, then measured the energy levels of graphene’s electrons. The quantum fractal appeared in all its glory. “Suddenly it went from a fantasy of mathematicians’ imagination to something real,” Zhytomirskaya said. “It becomes very volatile.”
