Relaxation in nonlinear systems, nonconvergent infinite continued fractions and sensitive relaxation processes

The Mori-Lee treatment of linear response theory demonstrates that the Laplace transform of any relaxation function of a dynamical variable can be expressed as a continued fraction. For certain simple nonlinear systems, the continued fraction representation of the relaxation functions cannot be evaluated perturbatively. It turns out that many body systems with even a single on-site nonlinearity can dramatically alter the relaxation behavior in such systems. We argue that nonperturbative continued fractions in the Mori-Lee formalism are necessarily associated with systems that exhibit relaxation that is sensitive to the presence of nonlinearities.