2008/04/03 by Ivan G. Szendro, Juan M. Lopez, J.M. López +2
Mathematics · Physics and Astronomy · #Chaotic #Chaotic scattering #Computer science #Geometry #Homogeneous space #Mathematics #Physics #Quantum mechanics #Scale invariance #Scaling #Scientific Research and Discoveries #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1103/physreve.78.036202
10 pages, 10 figs, RevTeX, submitted to PRE
arxiv created 2008/04/03 · openalex publication_date 2008/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that are selected by the particular configuration of disorder. The spatiotemporal behavior of typical perturbations deltau(x,t) is analyzed in terms of the Hopf-Cole transform h(x,t) identical withlnmid R:deltau(x,t)mid R: . Our analysis shows that the associated surface h(x,t) self-organizes into a faceted structure with scale-invariant correlations. Scaling analysis of critical roughening exponents reveals that there are three different universality classes for error propagation in disordered chaotic systems that correspond to different symmetries of the underlying disorder. Our conclusions are based on numerical simulations of disordered lattices of coupled chaotic elements and equations for diffusion in random potentials. We propose a phenomenological stochastic field theory that gives some insights on the path for a generalization of these results for a broad class of disordered extended systems exhibiting space-time chaos.