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.