19 citations · 73 across the 12 of their papers we have counts for
5 papers · 1 filter
On the Reduced Hartree-Fock Equations with a Small Anderson Type Background Charge Distribution
Ilias Chenn, Shiwen Zhang
We demonstrate that the reduced Hartree-Fock equation (REHF) with a small Anderson type background charge distribution has an unique stationary solution by explicitly computing a s…
The landscape law for tight binding Hamiltonians
Douglas N. Arnold, Marcel Filoche, Svitlana Mayboroda +2
The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schrödinger operator on . In particular, we establish upper and lower bound…
Sharp estimates for the integrated density of states in Anderson tight-binding models
Perceval Desforges, Svitlana Mayboroda, Shiwen Zhang +4
Recent work [G. David, M. Filoche, and S. Mayboroda, arXiv:1909.10558[Adv. Math. (to be published)]] has proved the existence of bounds from above and below for the Integrated Dens…
The exponential decay of eigenfunctions for tight binding Hamiltonians via landscape and dual landscape functions
Wei Wang, Shiwen Zhang
We consider the discrete Schrödinger operator on a cube , with periodic or Dirichlet (simple) boundary conditions. We use a hidden landscape functio…
Large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles
Rui Han, Shiwen Zhang
We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates which lead t…