Related papers: The scaling limit of eigenfunctions for 1d random …
We consider the 1d Schr\"odinger operator with decaying random potential, and study the joint scaling limit of the eigenvalues and the measures associated with the corresponding eigenfunctions which is based on the formulation by…
We study the level statistics of one-dimensional Schr\"odinger operator with random potential decaying like $x^{-\alpha}$ at infinity. We consider the point process $\xi_L$ consisting of the rescaled eigenvalues and show that : (i)(ac…
We consider two models of one-dimensional discrete random Schrodinger operators (H_n \psi)_l ={\psi}_{l-1}+{\psi}_{l +1}+v_l {\psi}_l, {\psi}_0={\psi}_{n+1}=0 in the cases v_k=\sigma {\omega}_k/\sqrt{n} and v_k=\sigma {\omega}_k/ \sqrt{k}.…
We study the 1d Schr\"odinger operators with alloy type random supercritical decaying potential and prove the clock convergence for the local statistics of eigenvalues. We also consider, besides the standard i.i.d. case, more general ones…
Consider the random Schr\"odinger operator $H_n$ defined on $\{0,1,\cdots,n\}\subset\mathbb{Z}$ $$ (H_n\psi)_\ell=\psi_{\ell-1,n}+\psi_{\ell+1,n}+\sigma\frac{\omega_\ell}{a_{\ell,n}}\psi_{\ell,n},\quad \psi_0=\psi_{n+1}=0, $$ where…
We study the eigenvalues of Schr\"odinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where $V$ decays exponentially at infinity.
As an extension to the paper by Breuer, Grinshpon, and White \cite{B}, we study the linear statistics for the eigenvalues of the Schr\"odinger operator with random decaying potential with order ${\cal O}(x^{-\alpha})$ ($\alpha>0$) at…
In this paper, I consider one-dimensional periodic Schr{\"o}dinger operators perturbed by a slowly decaying potential. In the adiabatic limit, I give an asymptotic expansion of the eigenvalues in the gaps of the periodic operator. When one…
Estimates for the total multiplicity of eigenvalues for Schr\"odinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.
For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the…
We study fluctuations of polynomial linear statistics for discrete Schr\"odinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth…
We study decaying half-line Schr\"odinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral…
We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…
We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.
We consider the 1d Schr\"odinger operators with random decaying potentials where the spectrum is pure point(sub-critical case). We show that the point process composed of the rescaled eivenvalues, together with those zero points of the…
We study a class of Schr\"odinger operators on $\Z^2$ with a random potential decaying as $|x|^{-\dex}$, $0<\dex\leq\frac12$, in the limit of small disorder strength $\lambda$. For the critical exponent $\dex=\frac12$, we prove that the…
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…
The purpose of the present work is to establish decorrelation estimates at distinct energies for some random Schr\"odinger operator in dimension one. In particular, we establish the result for some random operators on the continuum with…
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the…
We consider Schr\"odinger operator with random decaying potential on $\ell^2 ({\bf Z}^d)$ and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal eigenvalues, after rescaling, converges…