Related papers: Arithmetic spectral transition for the unitary alm…
The derivation procedure of exact ground-states for the periodic Anderson model (PAM) in restricted regions of the parameter space and D=2 dimensions using plaquette operators is presented in detail. Using this procedure, we are reporting…
Roughly half of numerical investigations of the Anderson transition are based on consideration of an associated quasi-1D system and postulation of one-parameter scaling for the minimal Lyapunov exponent. If this algorithm is taken…
We consider a modulated magnetic field, $B(t) = B_0 +\varepsilon f(\omega t)$, perpendicular to a fixed plane, where $B_0$ is constant, $\varepsilon>0$ and $f$ a periodic function on the torus ${\mathbb T}^n$. Our aim is to study classical…
We consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. We establish Anderson localization for this type of operator under the assumption that the coupling constant is…
We consider the Schr\"odinger operator on the real line with a $N\ts N$ matrix valued periodic potential, N>1. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov…
We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator…
We obtain the sharp arithmetic Gordon's theorem: that is, absence of eigenvalues on the set of energies with Lyapunov exponent bounded by the exponential rate of approximation of frequency by the rationals, for a large class of…
The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…
Control of orbital angular momentum (OAM) in optical fields has seen tremendous growth of late, with a myriad of tools existing for their creation and detection. What has been lacking is the ability to arbitrarily modify the OAM spectrum of…
In this paper we study the parabolic Anderson equation \partial u(x,t)/\partial t=\kappa\Delta u(x,t)+\xi(x,t)u(x,t), x\in\Z^d, t\geq 0, where the u-field and the \xi-field are \R-valued, \kappa \in [0,\infty) is the diffusion constant, and…
Let $d\gamma(x)\equiv\pi^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(\gamma)$ of Mauceri and Meda via commutators of…
It has been shown by Voros \cite {V} that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schr\"odinger operator with potential $q^{2M}$, $M>1$) is a fixed point of an explicit non-linear transformation. We show that…
We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal…
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in…
We give a precise description of spectra of the Maryland model $ (h_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+ \lambda \tan \pi(\theta+n\alpha)u_n$ for all values of parameters. We introduce an arithmetically defined index $\delta…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov's theorem from differential geometry, we propose an iterative…
We develop a sharp palindromic argument for general 1D operators, that proves absence of semi-uniform localization in the regime of exponential symmetry-based resonances. This provides the first examples of operators with dynamical…
For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in \cite{HiSeSu}. In this paper, as an application of the spectral mapping theorem, we investigate the spectrum of a one-dimensional…
The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable measure of the localisation length. The Lyapunov exponent…