  Many experimentally relevant systems are quasi-one-dimensional, consisting of
nearly decoupled chains. In these systems, there is a natural separation of
scales between the strong intra-chain interactions and the weak interchain
coupling. When the intra-chain interactions are integrable, weak interchain
couplings play a crucial part in thermalizing the system. Here, we develop a
Boltzmann-equation formalism involving a collision integral that is
asymptotically exact for any interacting integrable system, and apply it to
develop a quantitative theory of relaxation in coupled Bose gases in the
experimentally relevant Newton's cradle setup. We find that relaxation involves
a broad spectrum of timescales. We provide evidence that the Markov process
governing relaxation at late times is gapless; thus, the approach to
equilibrium is generally non-exponential, even for spatially uniform
perturbations.
