Kazuki Ikeda (Osaka) – Mathematics and Physics of Hofstadter Butterfly, and Quantum Computation 

Speaker: Kazuki Ikeda from Osaka university.

Title: Mathematics and Physics of Hofstadter Butterfly,

and Quantum Computation

Abstract:

Quantum Hall effect (QHE) is one of the most important phenomena in condensed matter physics, high energy physics, and mathematical physics. Especially QHE is the crucial for the recent advances in symmetry protected topological phase and topological quantum computation. In my talk, I’ll explain the mathematics and physics of QHE by the following plan.

In part 1, I explain mathematical foundation of quantum Hall effect and Hofstadter butterfly from a viewpoint of the Langlands program, which is the “grand unification theory” of mathematics. In part 2, I address the Hofstadter problem on a lattice with defects. I show the energy spectra associated with the localised current around the defect appear in the energy gaps of fractal butterfly. In part 3, I describe application of adiabatic quantum computation to the material search.