Mobility Edge in a Model One-Dimensional Potential

We show that a one-dimensional tight-binding electron moving in a slowly varying potential, ${V}_{n}=\ensuremath{\lambda}cos(\ensuremath{\alpha}{n}^{\ensuremath{\nu}})$, where $n$ is the site index and $0<\ensuremath{\nu}<1$, has a mobility edge in its spectrum provided that $2\ensuremath{\lambda}$ is smaller than the total unperturbed bandwidth of the system. We study the nature of the localized and extended eigenstates of this system as a function of $\ensuremath{\lambda}$ and $\ensuremath{\nu}$.