Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 134, Issue 2, Pages 381-400Publisher
SPRINGER
DOI: 10.1007/s10955-008-9675-z
Keywords
Lorenz system; Non-equilibrium steady states; Ruelle response theory; Kramers-Kronig relations; Sum rules; Axiom A; Singular hyperbolic system; Harmonic generation; Susceptibility; Numerical simulation; Time series analysis; Spectrum; Periodic forcing; Climate
Categories
Ask authors/readers for more resources
Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available