CHAOS AND LINEAR-RESPONSE - ANALYSIS OF THE SHORT-TIME, INTERMEDIATE-TIME, AND LONG-TIME REGIME

We study the response of a classical Hamiltonian system to a weak pert urbation in the regime where the dynamics is mixing, with the purpose of critically examining both the foundation of the Kubo linear respons e theory (LRT) and van Kampen's well known objections to LRT [Phys. No rv. 5, 279 (1971)]. Although the exactness of LRT for short times is n ot surprising, we prove that for the class of model studied here the L RT must also become accurate in the limit of long times, even for macr oscopically large external perturbations. Hence, if the LRT breaks dow n, the breakdown occurs in the region of intermediate times. We also s how that, for a given system, if any macroscopic linear response exist s, it must coincide with Kubo LRT; thus, if a generic system responds nonlinearly to an external perturbation, this nonlinear response is ob servable only in an intermediate-time range. Numerical calculations ca rried out on some model systems with only a few degrees of freedom sup port these arguments.