2015/09/25 by Giorgio Turchetti, G. Turchetti, Turchetti, Giorgio +9
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Autocorrelation #Chaotic #Chaotic Dynamics (nlin.CD) #Exponential decay #Exponential function #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Integrable system #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Multiplicative function #Multiplicative noise #Phase space #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Statistics #nlin.CD
paper · pdf · doi:10.48550/arxiv.1509.07738
22 pages, 3 figures
openalex publication_date 2015/09/25 · arxiv created 2016/12/09 · arxiv updated 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyse the asymptotic growth of the error for Hamiltonian flows due to\nsmall random perturbations. We compare the forward error with the reversibility\nerror, showing their equivalence for linear flows on a compact phase space. The\nforward error, given by the root mean square deviation \σ(t) of the noisy\nflow, grows according to a power law if the system is integrable and according\nto an exponential law if it is chaotic.\n The autocorrelation and the fidelity, defined as the correlation of the\nperturbed flow with respect to the unperturbed one, exhibit an exponential\ndecay as \exp\(-\σ2(t)\). Some numerical examples such as the\nanharmonic oscillator and the H 'enon Heiles model confirm these results. We\nfinally consider the effect of the observational noise on an integrable system,\nand show that the decay of correlations can only be observed after a sequence\nof measurements and that the multiplicative noise is more effective if the\ndelay between two measurements is large.\n