Seminari by Raffaele Resta (IOM-CNR, Trieste)

The paradigmatic geometrical observable is the macroscopic electric polarization P of a crystalline insulator: since the early 1990s it is known that P is a geometric phase of the ground-state wavefunction. The geometrical nature of several other observables has been elucidated over the years: most notably orbital magnetization and anomalous Hall conductivity. In some special cases a geometrical observable is quantized, and becomes therefore topological: extremely robust with respect to perturbations, and measurable in principle with infinite precision.

In this talk I will start explaining what “geometrical” means in quantum mechanics. Then I will outline the main features of P and of a few other observables.

The talk will be addressed to Master/PhD students as well as to researchers.