相关论文: Single parameter scaling in one-dimensional locali…
We investigate the short-distance statistics of the local density of states nu in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function P(nu) can be recovered…
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…
We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the…
The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant…
We consider the one-dimensional Schr\"odinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function $\psi(x)$, known in the literature as the "generalized Lyapunov exponent"; this…
We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for…
Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…
We exploit the analogy between dynamics of inertial particle pair separation in a random-in-time flow and the Anderson model of a quantum particle on the line in a spatially random real-valued potential. Thereby we get an exact formula for…
In this work we present a theoretical and numerical study of the behaviour of the maximum Lyapunov exponent for a generic coupled-map-lattice in the weak-coupling regime. We explain the observed results by introducing a suitable…
The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…
Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as…
It is known that a one-dimensional quantum particle is localized when subjected to an arbitrarily weak random potential. It is conjectured that localization also occurs for an arbitrarily weak potential generated from the nonlinear…
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…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…
We numerically study the Anderson localization of weekly interacting Bose-Einstein condensate in a one-dimensional disordered potential. We show that two parameters are needed to completely describe such system, and the density profile of…
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…
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…
I consider random Schr\"odinger operators with exponentially decaying single site potential, which is allowed to change sign. For this model, I prove Anderson localization both in the sense of exponentially decaying eigenfunctions and…
We consider random Schr\"{o}dinger operators on $\ell^2(\mathbb{Z}^d)$ when the distribution of single site potentials is $\alpha$-H\"{o}lder continuous ($0<\alpha\leq 1$). In localized regime we study the distribution of eigenfunctions…
We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to…