Almost Mathieu operator
In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by acting as a self-adjoint operator on the Hilbert space . Here are parameters. In pure mathematics, its importance comes from the fact of being one of the best-understood examples of an ergodic Schrödinger operator. For example, three problems (now all solved) of Barry Simon's fifteen problems about Schrödinger operators "for the twenty-first century" featured the almost Mathieu operator. In physics, the almost Mathieu operators can be used to study metal to insulator transitions like in the Aubry–André model. For , the almost Mathieu operator is sometimes called Harper's equation. (Wikipedia).
