'Ten Martini' Proof Uses Number Theory to Explain Quantum Fractals
15 days ago
- #quantum-mechanics
- #number-theory
- #fractals
- Douglas Hofstadter discovered the Hofstadter butterfly while studying quantum mechanics with a calculator.
- The Hofstadter butterfly is a fractal pattern representing electron energy levels in a magnetic field.
- The 'Ten Martini' conjecture proposed that energy levels form a Cantor set for irrational values of alpha.
- Artur Avila and Svetlana Jitomirskaya proved the conjecture in 2005, earning a Fields Medal for Avila.
- Lingrui Ge and collaborators expanded Avila's global theory to solve broader versions of the problem.
- The Hofstadter butterfly was experimentally observed in graphene, confirming its real-world relevance.