Nonanalytic enhancement of the charge transfer from adatom to   one-dimensional semiconductor superlattice and optical absorption spectrum
  The charge transfer from an adatom to a semiconductor substrate of one-dimensional quantum dot array is evaluated theoretically. Due to the Van Hove singularity in the density of electron states at the band edges, the charge transfer decay rate is enhanced nonanalytically in terms of the coupling constant $g$ as $g^{4/3}$. The optical absorption spectrum for the ionization of a core level electron of the adatom to the conduction band is also calculated. The reversible non-Markovian process and irreversible Markovian process in the time evolution of the adatom localized state manifest themselves in the absorption spectrum through the branch point and pole contributions, respectively. 
Satoshi Tanaka, Sterling Garmon, Tomio Petrosky