Related papers: Lyapunov exponents in 1d disordered system with lo…
We consider the solution $u$ to the one-dimensional parabolic Anderson model with homogeneous initial condition $u(0, \cdot) \equiv 1$, arbitrary drift and a time-independent potential bounded from above. Under ergodicity and independence…
Training large deep neural networks is resource intensive. This study investigates whether Lyapunov exponents can accelerate this process by aiding in the selection of hyperparameters. To study this I formulate an optimization problem using…
This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance…
The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed…
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 establish exponential localization for a two-particle Anderson model in a Euclidean space ${\mathbb R}^{d}$, $d\ge 1$, in presence of a non-trivial short-range interaction and a random external potential of the alloy type. Specifically,…
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned to never being absorbed, the $Q$-process, into the…
We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are…
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…
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering…
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 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…
Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as…
We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length \sigma_R. For speckle potentials the Fourier transform of the…
We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a…
We consider two bidimensional random models characterised by the following features: a) their Hamiltonians are separable in polar coordinates and b) the random part of the potential depends either on the angular coordinate or on the radial…
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood. We provide conditions under which the perturbed system is ergodic and admits a…
For a one-dimensional discrete Schr\"odinger operator with a weakly coupled potential given by a strongly mixing dynamical system with power law decay of correlations, we derive for all energies including the band edges and the band center…