相关论文: Regularity of the density of states for random Dir…
We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main…
Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
We study the special case of $n\times n$ 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix $J=(-W^2\triangle+1)^{-1}$. Assuming that $n\ge CW\log W\gg 1$, we prove that the averaged…
We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the…
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…
Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schr\"odinger operators, and established a quantitative form of continuity in…
A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong…
We consider the random Schr\"odinger operator on $\mathbb{R}$ obtained by perturbing the Laplacian with a white noise. We prove that Anderson localization holds for this operator: almost surely the spectral measure is pure point and the…
We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose…
We prove estimates on the H\"older exponent of the density of states measure for discrete Schr\"odinger operators with potential of the form $V(n) = \lambda(\lfloor(n+1)\beta\rfloor - \lfloor n\beta\rfloor)$, with $\lambda$ large enough,…
In this paper, the average density of states (ADOS) with a binary alloy disorder in disordered graphene systems are calculated based on the recursion method. We observe an obvious resonant peak caused by interactions with surrounding…
We continue our study of the dependence of the density of states measure and related spectral functions of Schr\"odinger operators on the potential. Whereas our earlier work focused on random Schr\"odinger operators, we extend these results…
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 Density of States (IDOS) of the Schr\"odinger operator…
In this work, we study the Anderson model on graphs with Ahlfors $\alpha$-regular volume growth. We show that, under mild regularity assumptions of the random distribution, Lifshitz-tail type estimates near the bottom of the spectrum lead…
We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it…
For the iterations of $x\mapsto |x-\theta|$ random functions with Lipschitz number one, we represent the dynamics as a Markov chain and prove its convergence under mild conditions. We also demonstrate that the Wasserstein metric of any two…
We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical rigidity argument.
We continue the investigations of Kirsch, Metzger and the second-named author [J. Stat. Phys. 143, 1035--1054 (2011)] on spectral properties of a certain type of random block operators. In particular, we establish an alternative version of…
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…