Thermalization in a quasi-1D ultracold bosonic gas

TL;DR

This paper investigates how quantum correlations suppress thermalization in a one-dimensional ultracold bosonic gas, highlighting the role of virtual excitations and three-body interactions in the process.

Contribution

It demonstrates that strong quantum correlations significantly suppress three-body collisions, preventing thermalization in 1D bosonic gases even when two-body collisions are energetically suppressed.

Findings

Three-body elastic interactions are suppressed by quantum correlations.

Thermalization is prevented by strong correlations rather than the absence of two-body collisions.

Suppression factor scales as (k/c)^{12} proportional to the square of the three-body correlation function.

Abstract

We study the collisional processes that can lead to thermalization in one-dimensional systems. For two body collisions excitations of transverse modes are the prerequisite for energy exchange and thermalzation. 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 to the two-body coupling constant $c$ the three-particle scattering state is suppressed by a factor of $(k/c)^{12}$, which is proportional to $\gamma ^{12}$, that is to the square of the three-body correlation function at zero distance in the limit of the Lieb-Liniger parameter $\gamma \gg 1$. This demonstrates that in one dimensional quantum systems it is not the freeze-out of two body collisions but the strong quantum correlations which ensures absence of thermalization on experimentally relevant time scales.