ERC Workshop on Geometric Partial Differential Equations

# Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions

speaker: Adriano Pisante (Dipartimento di Matematica, Università di Roma "La Sapienza")

abstract: We consider a periodic Schr\"{o}dinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional introduced by Marzari-Vanderbilt and we prove some results about the existence and exponential localization of its minimizers, in dimension $d \leq 3$. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds.

timetable:
Wed 12 Sep, 9:30 - 10:15, Aula Magna Dipartimento di Matematica
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