Categoria:
Seminari di Fisica Matematica
Data e ora inizio evento:
Data e ora fine evento:
Aula:
Sala di Consiglio
Sede:
Dipartimento di Matematica Guido Castelnuovo, Università Sapienza Roma
Speaker:
Stefan Teufel (Eberhard-Karls Universität Tübingen)
The spectrum of periodic operators can be computed analytically and also approximated numerically using Bloch-Floquet theory, i.e. discrete Fourier transformation. For quasi-periodic operators no such general approach is available. In my talk I will first present a method for approximating the spectrum of general short-range infinite-volume operators on discrete sets with two-sided error control, using only data from finite-sized local patches. For operators with the additional property of finite local complexity this yields an explicit algorithm for approximating the spectrum numerically and allows, in particular, for computer assisted proofs of spectral gaps in such systems. As examples I discuss the p_x p_y-model and the discrete magnetic Laplacian on the two-dimensional quasi-periodic Ammann-Beenker tiling. This is based on joint work with Paul Hege and Massimo Moscolari (Physical Review B 2022 and Mathematics of Computation 2025).
Contatti/Organizzatori: