Breakdown of integrability in a quasi-one-dimensional ultracold bosonic   gas
  We demonstrate that virtual excitations of higher radial modes in an atomic Bose gas in a tightly confining waveguide result in effective three-body collisions that violate integrability in this quasi-one-dimensional quantum system and give rise to thermalization. The estimated thermalization rates are consistent with recent experimental results in quasi-1D dynamics of ultracold atoms. 
I.E. Mazets, T. Schumm, J. Schmiedmayer