PROBING MICROSCOPIC CHAOTIC DYNAMICS BY OBSERVING MACROSCOPIC TRANSPORT PROCESSES

We derive the Kramers equation, namely, the Fokker-Planck equation for an oscillator, from a completely deterministic picture. The oscillato r is coupled to a ''booster'', i.e., a deterministic system in a fully chaotic state, wherein diffusion is derived from the sensitive depend ence of chaos on initial conditions and friction is a consequence of t he linear response of the booster to the action exerted on it by the o scillator. To deal with the Hamiltonian nature of the system of intere st and of its coupling to the booster, we extend the earlier theoretic al derivation of macroscopic transport coefficients from deterministic dynamics. We show that the frequency of the oscillator can be tuned t o the microscopic frequencies of the booster without affecting the can onical nature of the ''macroscopic'' statistics. The theoretical predi ctions are supported by numerical simulations.