Asymptotic analysis of the localization spread and polarizability of 1-D noninteracting electrons

摘要

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 λ _(1βγ) 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 λ _(βγ) 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.