相关论文: Comment on `Exact analytical solution for the gene…
The Anderson localization problem in one and two dimensions is solved analytically via the calculation of the generalized Lyapunov exponents. This is achieved by making use of signal theory. The phase diagram can be analyzed in this way. In…
We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical…
Subsequent to the ideas presented in our previous papers [J.Phys.: Condens. Matter {\bf 14} (2002) 13777 and Eur. Phys. J. B {\bf 42} (2004) 529], we discuss here in detail a new analytical approach to calculating the phase-diagram for the…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for…
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…
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…
We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various…
The generalized Lyapunov exponents describe the growth of the second moments for a particular solution of the quasi-1D Schroedinger equation with initial conditions on the left end. Their possible application in the Anderson transition…
Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov…
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…
We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson…
The possible existence of the Anderson transition in 2D systems without interaction and spin-orbit effects (such as the usual Anderson model) becomes recently a subject of controversy in the literature. Comparative analysis of approaches…
The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…
It is considered an equation for the Lyapunov exponent $% \gamma $ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of…
The Lyapunov exponents for Anderson localization are studied in a one dimensional disordered system. A random Gaussian potential with the power law decay $\sim 1/|x|^q$ of the correlation function is considered. The exponential growth of…
Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be…