Nell'ambito dei Tè di Matematica, per celebrare il pensionamento di
Elisabetta Scoppola, mercoledì *29 ottobre* alle *ore 16:00*, Fabio
Martinelli terrà un seminario dal titolo *"An Introduction to the
Mathematical Theory of Anderson Localization"*.
Abstract: In 1958, the physicist P. W. Anderson published the paper
"Absence of Diffusion in Certain Random Lattices," which contributed to
winning him the Nobel Prize in 1977 for the discovery of the phenomenon now
known as "Anderson localization." In the simplest case, Anderson
localization states that a Schroedinger operator with a random potential
on, e.g., a d-dimensional lattice has a pure-point spectrum with
exponentially localized eigenstates if the randomness of the potential is
sufficiently strong. In his Nobel lecture Anderson said "...*Localization
was a different matter: very few believed it at the time, and even fewer
saw its importance; among those who failed to fully understand it at first
was certainly its author. It has yet to receive adequate mathematical
treatment, and one has to resort to the indignity of numerical simulations
to settle even the simplest questions about it." *Proving Anderson
localization was one of the great problems in mathematical physics in the
early 1980s, and E. Scoppola greatly contributed to its solution in the
hard case d > 1. On the occasion of her retirement, I will provide a brief
overview of the Anderson model and eigenfunction localization, as well as
some of the more recent developments. If time allows, I will also try to
describe how the basic multiscale analysis underlying the proof of Anderson
localization can be applied to other, quite different, contexts.
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e
Fisica dell'Università di Roma Tre, Lungotevere Dante 476, *aula M1*.