Asymptotic analysis of the localization spread and polarizability of 1-D noninteracting electrons
Résumé
According to the modern Theory of the Insulating State [Resta, J Chem Phys 2006, 124, 104104], the metallic behavior of a N-electron system with open boundary conditions is characterized by a localization spread λβγ diverging in the thermodynamic limit. This quantity, which is the second-moment cumulant of the position operator (per electron), cannot in general be evaluated in closed form but for simple model systems. In this article, we perform an asymptotic analysis of λβγ for a gas of N non-interacting electrons in a 1-Dimensional box and a Hückel chain of N equivalent sites. The asymptotic behavior of the closely related polarizability tensor is also investigated for these exactly solvable models.