Single-particle mobility edge without disorder

The existence of localization and mobility edges in one-dimensional lattices is commonly thought to depend on disorder (or quasidisorder). We investigate properties a disorder-free lattice subject an equally spaced electric field. analytically show that, even though the model has no quenched disorder, this system manifests exact edge regime extends weak fields, contrast gigantic field for usual Stark lattice. For strong Wannier-Stark ladder recovered, number localized eigenstates inversely proportional spacing. Moreover, we study time dependence initially excitation dynamically probe edge.