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

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 beta 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 beta for a gas of N non-interacting electrons in a 1-Dimensional box and a Huckel chain of N equivalent sites. The asymptotic behavior of the closely related polarizability tensor is also investigated for these exactly solvable models. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011