Thermalization in a quasi-one-dimensional ultracold bosonic gas

Abstract

We study the collisional processes that can lead to thermalization in one-dimensional (1D) systems. For two-body collisions, excitations of transverse modes are the prerequisite for energy exchange and thermalization. At very low temperatures, excitations of transverse modes are exponentially suppressed, thermalization by two-body collisions stops and the system should become integrable. In quantum mechanics, virtual excitations of higher radial modes are possible. These virtually excited radial modes give rise to effective three-body velocity-changing collisions, which lead to thermalization. We show that these three-body elastic interactions are suppressed by pairwise quantum correlations when approaching the strongly correlated regime. If the relative momentum k is small compared with the two-body coupling constant c, the three-particle scattering state is suppressed by a factor of (k/c)12, which is proportional to γ−12, that is, to the square of the three-body correlation function at zero distance in the limit of the Lieb–Liniger parameter γ≫1. This demonstrates that in 1D quantum systems, it is not the freeze-out of two-body collisions but the strong quantum correlations that ensure absence of thermalization on experimentally relevant time scales.