title: Exponential decay properties of Wannier functions and related quantities.
abstract: The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of nonorthonormal Wannier-like functions.
authors.affiliation: Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-0849, USA.
authors.forename: L
authors.initials: L
authors.lastname: He
authors.forename: D
authors.initials: D
authors.lastname: Vanderbilt