Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

Nenciu, Gheorghe

Optimally localized Wannier functions for quasi one-dimensional nonperiodic systems

It is proved that for general, not necessarily periodic one-dimensional systems, the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial localization as the corresponding spectral projection. As a consequence, an eigenbasis of the band position operator provides a basis of optimally localized Wannier functions.