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CATEGORIES:fc300's list
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:TALK18631AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/18631
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 linear and the second h
armonic response for the perturbed Lorenz 63 syste
m\, by showing that numerical simulations agree up
to high degree of accuracy with the theoretical p
redictions. Some new theoretical results\, showing
how to derive asymptotic behaviours and how to ob
tain recursively harmonic generation susceptibilit
ies for general observables\, are also presented.
Our findings confirm the conceptual validity of th
e nonlinear response theory\, suggest that the the
ory can be extended for more general non equilibri
um steady state systems\, and shed new light on th
e applicability of very general tools\, based only
upon the principle of causality\, for diagnosing
the behaviour of perturbed chaotic systems and rec
onstructing their output signals\, in situations w
here the fluctuation-dissipation relation is not o
f great help.\n\n\n
LOCATION:Centre for Mathematical Sciences\, Meeting Room 14
.
CONTACT:Dr. Fenwick Cooper
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