相关论文: Single parameter scaling in one-dimensional locali…
The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of the…
Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance…
We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection…
We numerically study the distribution function of the conductivity (transmission) in the one-dimensional tight-binding Anderson model in the region of fluctuation states. We show that while single parameter scaling in this region is not…
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…
Validity of the single parameter scaling (SPS) in one dimensional Anderson model with purely off-diagonal disorder is being studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS.…
Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new…
We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this…
The cumulants of the logarithm of the conductance (lng) in the localized regime in the one-dimensional Anderson model are calculated exactly in the second Born approximation for weak disorder. Only the first two cumulants turn out to ne…
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…
Localization of acoustic waves in a one dimensional water duct containing many randomly distributed air filled blocks is studied. Both the Lyapunov exponent and its variance are computed. Their statistical properties are also explored…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-{\em D} random periodic-on-average systems. States from pass bands and band edges of the underlying band…
We study a unitary version of the one-dimensional Anderson model, given by a five diagonal deterministic unitary operator multiplicatively perturbed by a random phase matrix. We fully characterize positivity and vanishing of the Lyapunov…
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…
Statistical and scaling properties of the Lyapunov exponent for a tight-binding model with the diagonal disorder described by a dichotomic process are considered near the band edge. The effect of correlations on scaling properties is…
We prove spectral and dynamical localization for a one-dimensional Dirac operator to which is added an ergodic random potential, with a discussion on the different types of potential. We use scattering properties to prove the positivity of…
Advances in material growth methods have renewed the interest in localization of one-dimensional systems in the presence of scale-free long-range correlated disorder potentials. We analyze the validity of single parameter scaling for the…
The one parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show this theory can be adapted to the context of quantum chaos provided that the classical phase space…