Ballistic particle transport and Drude weight in mono-atomic gases

Owing to the fact that, in the particular case of non-relativistic mono-atomic gases, the particle current operator is proportional to the operator of the total momentum, the particle transport in such systems is always ballistic and fully characterized by a Drude weight $\Delta$. The Drude weight can be calculated as a generalized susceptibility from a generalized Gibbs ensemble. For the case of the integrable one dimensional Bose gas with contact interactions this susceptibility can be obtained exactly and explicitly from a generalized Yang-Yang thermodynamic formalism. The result is temperature independent and given by $\Delta = 2 \pi D = 2 k_F$, where $D$ is the density of the gas and $k_F$ its Fermi momentum. Our expression, derived by first principle calculations, confirms a more involved formula obtained heuristically by means of generalized hydrodynamics.