Thermalization of Interacting Quasi-One-Dimensional Systems

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 intrachain interactions and the weak interchain coupling. When the intrachain 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 nonexponential, even for spatially uniform perturbations.

Automated summary

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains, where weak interchain couplings play a crucial role in thermalizing the system. We developed a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and applied it to study relaxation in coupled Bose gases in the Newton's cradle setup. We found that relaxation involves a broad spectrum of timescales and the Markov process governing relaxation at late times is gapless, leading to nonexponential approach to equilibrium even for spatially uniform perturbations.