Thermalization in a one-dimensional integrable system

We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional integrable system (a quasicondensate of ultra-cold, weakly-interacting bosonic atoms being studied as a definite example). These results may seem counterintuitive because the physical system is integrable in both the quantum and classical (mean-field) descriptions. However, we find a class of initial conditions that admits the relaxation of distributions of single-particle observables to the equilibrium state very close to the Bose-Einstein thermal distribution of Bogoliubov quasiparticles. Our numerical results allow us to explain experimentally observed thermalization in one-dimensional ultracold atomic gases on a short (~1 ms) time scale.