Gilad Sofer (Technion)
Abstract: Sturmian Hamiltonians appear in mathematical physics as popular models for one-dimensional quasicrystals. This family of discrete quasiperiodic Schrödinger operators, including the well known Fibonacci Hamiltonian, is widely studied for its interesting spectral properties. We study metric analogues of these systems, by considering families of quasiperiodic metric graphs whose local geometric structure is determined by Sturmian sequences. We show that these graphs share many spectral properties with their discrete Sturmian counterparts. For instance, their spectra can be obtained as the limiting spectra of an appropriate sequence of periodic approximations. We also point at several unique features of these models, which are distinct to the metric setting.
The talk is based on a joint work in progress with Ram Band.
