Hamiltonian chaos acts like a finite energy reservoir: accuracy of the Fokker-Planck approximation.
The Hamiltonian dynamics of slow variables coupled to fast degrees of freedom is modeled by an effective stochastic differential equation. Formal perturbation expansions, involving a Markov approximation, yield a Fokker-Planck equation in the slow subspace which respects conservation of energy. A detailed numerical and analytical analysis of suitable model systems demonstrates the feasibility of obtaining the system specific drift and diffusion terms and the accuracy of the stochastic approximation on all time scales. Non-Markovian and non-Gaussian features of the fast variables are negligible.
Riegert
Anja
A
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D 01187 Dresden, Germany. riegert@mpipks-dresden.mpg.de
Baba
Nilüfer
N
Gelfert
Katrin
K
Just
Wolfram
W
Kantz
Holger
H