19 citations · 73 across the 12 of their papers we have counts for
12 papers
Approximating the ground state eigenvalue via the effective potential
Ilias Chenn, Wei Wang, Shiwen Zhang
In this paper, we study 1-d random Schrödinger operators on a finite interval with Dirichlet boundary conditions. We are interested in the approximation of the ground state energy…
On a Novel Effective Equation of the Reduced Hartree-Fock Theory
Ilias Chenn, Svitlana Mayboroda, Wei Wang +1
We show that there is an one-to-one correspondence between solutions to the Poisson-Landscape equations and the reduced Hartree-Fock equations in the semi-classical limit at low te…
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…
Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schrödinger operators
Fan Yang, Shiwen Zhang
We proved that Schrödinger operators with unbounded potentials have purely singular continuous spectrum on the set $\{E:…
Spectral Dimension for -almost periodic singular Jacobi operators and the extended Harper's model
Rui Han, Fan Yang, Shiwen Zhang
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition prope…
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…
The exact Power Law for Buffon's needle landing near some Random Cantor Sets
Shiwen Zhang
In this paper, we study the Favard length of some random Cantor sets of Hausdorff dimension 1. We start with a unit disk in the plane and replace the unit disk by disjoint subd…
Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators
Svetlana Jitomirskaya, Shiwen Zhang
We introduce a notion of -almost periodicity and prove quantitative lower spectral/quantum dynamical bounds for general bounded -almost periodic potentials. Applications incl…
Mixed spectral types for the one frequency discrete quasi-periodic Schrödinger operator
Shiwen Zhang
We consider a family of one frequency discrete analytic quasi-periodic Schrödinger operators which appear in [Bjer]. We show that this family provides an example of coexistence o…