• DOI:10.1103/PhysRevA.104.012207
• Corpus ID: 224704540

Sharp estimates for the integrated density of states in Anderson tight-binding models

@article{Desforges2020SharpEF,
  title={Sharp estimates for the integrated density of states in Anderson tight-binding models},
  author={Perceval Desforges and Svitlana Mayboroda and Shiwen Zhang and Guy David and Douglas N. Arnold and Wei Wang and Marcel Filoche},
  journal={Physical Review A},
  year={2020}
}

• Perceval Desforges, S. Mayboroda, +4 authors M. Filoche
• Published 19 October 2020
• Mathematics
• Physical Review A

Recent work [1] has proved the existence of bounds from above and below for the Integrated Density of States (IDOS) of the Schrodinger operator throughout the spectrum, called the \emph{Landscape Law}. These bounds involve dimensional constants whose optimal values are yet to be determined. Here, we investigate the accuracy of the Landscape Law in 1D and 2D tight-binding Anderson models, with binary or uniform random distributions. We show, in particular, that in 1D, the IDOS can be approximated with high accuracy through a single formula involving a remarkably simple multiplicative energy shift. In 2D, the same idea applies but the prefactor has to be changed between the bottom and top parts of the spectrum.