Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures*

We study relaxation in a one-dimensional two-mass mixture of hard-core particles. Special attention is paid to the region of light-to-heavy mass ratios around $m/M = \sqrt{5}-2 = 0.236\ldots$. At this mass ratio, each heavy-light-heavy subsystem constitutes a little known non-equal-mass generalization of Newton's 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, where integrability is especially prominent at the quantum level and leads to the famous ``scattering without diffraction'' phenomenon. The principal experimental application of our results is with two-specie mixtures in optical lattices, in which the effective masses---that can be controlled at will---are assumed to replace the real ones.