Traces of integrability in relaxation in one-dimensional two-mass mixtures

We study relaxation in a one-dimensional two-mass mixture of hard-core particles. A special attention is payed to the region of light-to-heavy mass ratios around m/M = sqrt(5)-2 = 0.236... . At this mass ratio, each heavy-light-heavy subsystem constitutes a little known non-equal-mass generalization of the Newton Cradle, and an anomalous slow-down of relaxation is expected as a result. We further list and classify all other instances of integrability in the one-dimensional three-body hard-core systems; there, integrability is especially prominent at the quantum level, leading to the famous "scattering without diffraction" phenomenon. The principal experimental application of our results is the two-specie mixtures in optical lattices; there, the effective masses---that can be controlled at will---are assumed to replace the real ones.