Localization by a Potential with Slowly Varying Period

In order to understand some discrepancies in the recent Letter of Griniasty and Fishman, a study has been made of localization by a one-dimensional potential with slowly varying period. Away from the band center, localization is produced by local regions in which the Bragg condition allows backward scattering, and the result agrees with that obtained from perturbation theory. The localization length increases as the band center is approached in a manner that cannot be obtained directly from perturbation theory. It is shown that rounding errors set an upper bound to the localization length that would be determined from numerical studies of such a problem.