Related papers: Spectral statistic for decaying random potentials

In this paper we consider some Anderson type models, with decaying randomness and the free parts having long range tails. The randomness may decay at different rates in different directions, though in majority of directions we require some…

We show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random…

We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian $\mathcal{H}_L$, with white noise potential, on a segment whose size $L$ is sent to infinity. We zoom around energy levels $E$ either of order $1$ (Bulk…

Let $\Lambda=\{\Lambda_0,\Lambda_1,\Lambda_2,\ldots\}$ be the point process that describes the edge scaling limit of either (i) "regular" beta-ensembles with inverse temperature $\beta>0$, or (ii) the top eigenvalues of Wishart or Gaussian…

In this work we consider the Anderson model on the $d$-dimensional lattice with the single site potential having singular distribution, mainly $\alpha$-H\"older continuous ones and show that the eigenvalue statistics is Poisson in the…

We prove weighted-$L^\infty$ and pointwise space-time decay estimates for weak solutions of a class of wave equations with time-independent potentials and subject to initial data, both of low regularity, satisfying given decay bounds at…

At Anderson critical points, the statistics of the two-point transmission $T_L$ for disordered samples of linear size $L$ is expected to be multifractal with the following properties [Janssen {\it et al} PRB 59, 15836 (1999)] : (i) the…

It is known that the eigenfunctions of a random Schr\"odinger operator on a strip decay exponentially, and that the rate of decay is not slower than prescribed by the slowest Lyapunov exponent. A variery of heuristic arguments suggest that…

We study the differential decay rate for the rare decay $\Lambda_b\to \Lambda(1520)(\to NK)\ell^+\ell^-$ where $\ell$ is a light lepton, as this decay mode can provide new and complementary constraints on the Wilson coefficients in $b\to…

In this article we study the problem of localization of eigenvalues for the non-homogeneous hierarchical Anderson model. More specifically, given the hierarchical Anderson model with spectral dimension $0<d<1$ with a random potential acting…

We study a random Schroedinger operator, the Laplacian with random Dirac delta potentials on a torus T^d_L = R^d/LZ^d, in the thermodynamic limit L\to\infty, for dimension d=2. The potentials are located on a randomly distorted lattice…

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…

We study the differential decay rate for the rare $\Lambda_b \to \Lambda (\to N \pi)\ell^+\ell^-$ transition, including a determination of the complete angular distribution, assuming unpolarized $\Lambda_b$ baryons. On the basis of a…

We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…

We investigate some bounds for the density of states in the pure point regime for the random Schr\"{o}dinger operators $H^{\omega}=-\Delta+\displaystyle\sum_{n\in\mathbb{Z}^d}a_nq_n(\omega)$, acting on $\ell^2(\mathbb{Z}^d)$, where…

We consider the Anderson model on the finite grid $G = \mathbb Z/L_1\mathbb Z\times\cdots\times\mathbb Z/L_d\mathbb Z$, defined by the random Hamiltonian $H_t=\Delta+tV$, where $\Delta$ is the discrete Laplacian and…

The unique time signature of the survival probability exactly at the exceptional point parameters is studied here for the hydrogen atom in strong static magnetic and electric fields. We show that indeed the survival probability…

In this note, we prove weighted resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at…

We investigate rare special dileptonic decays of $ \Lambda_b$, $\Sigma_b$ and $\Xi_b $ baryons in the Standard Model and context of the general Two-Higgs-Doublet Model with Type III. Specifically, we consider the decays $ \Lambda_b…

We consider the Laplace-Beltrami operator $\Delta_g$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_{\lambda}$ on $M$ associated with the spectral projection of $-\Delta_g$ onto the…