(Ir)regular singularities and Quantum Field Theory

Events

| seminar

Quantum Butterflies: Filling the white with colors

Speaker

Guiseppe De Nittis (Universidad Católica de Chile)

Abstract

Quantum Butterflies are spectra of certain self-adjoint operators in the noncommutative torus. These operators can be realized in “concrete” Hilbert spaces in different ways producing distinct differential/difference equations like the Harper equation, the Hofstadter equation or the (almost-)Mathieu equation. All these models share the same spectrum which is given by the celebrated Hofstadter butterfly. However, there are finer topological properties which complete the spectral picture and allow to distinguish the various models. These topological invariants can be coded with colors producing the colorful version of the Quantum Butterflies.