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CATEGORIES:Geophysical and Environmental Processes
SUMMARY:Dispersion Relations for the Nonlinear Response of
Chaotic Dynamical Systems - Valerio Lucarini\, De
partment of Physics\, University of Bologna
DTSTART;TZID=Europe/London:20090527T110000
DTEND;TZID=Europe/London:20090527T120000
UID:TALK18645AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18645
DESCRIPTION:Along the lines of the nonlinear response theory d
eveloped by Ruelle\, we prove under rather general
conditions that Kramers-Kronig dispersion relatio
ns and sum rules apply for a class of susceptibili
ties describing at any order of perturbation the r
esponse of Axiom A non equilibrium steady state sy
stems to weak monochromatic forcings. We then pres
ent a numerical evidence of the validity of these
integral relations for the\nlinear and the second
harmonic response for the perturbed Lorenz 63 syst
em\, by showing that numerical simulations agree u
p to high degree of accuracy with the theoretical
predictions. Some new theoretical results\, showin
g how to derive asymptotic behaviours and how to o
btain recursively harmonic generation susceptibili
ties for general observables\, are also presented.
Our findings confirm the conceptual validity of t
he nonlinear response theory\, suggest that the th
eory can be extended for more general non equilibr
ium steady state systems\, and shed new light on t
he applicability of very general tools\, based onl
y upon the principle of causality\, for diagnosing
the behaviour of perturbed chaotic systems and\nr
econstructing their output signals\, in situations
where the\nfluctuation-dissipation relation is no
t of great help.
LOCATION:MR14\, CMS
CONTACT:Doris Allen
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