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We outline a general formalism of hydrodynamics for quantum systems withmultiple particle species which undergo completely elastic scattering. In thethermodynamic limit, the complete kinematic data of the problem consists of theparticle content, the dispersion relations, and a universal dressingtransformation which accounts for interparticle interactions. We considerquantum integrable models and we focus on the one-dimensional fermionic Hubbardmodel. By linearizing hydrodynamic equations, we provide exact closed-formexpressions for Drude weights, generalized static charge susceptibilities andcharge-current correlators valid on hydrodynamic scale, represented as integralkernels operating diagonally in the space of mode numbers of thermodynamicexcitations. We find that, on hydrodynamic scales, Drude weights manifestlydisplay Onsager reciprocal relations even for generic (i.e. non-canonical)equilibrium states, and establish a generalized detailed balance condition fora general quantum integrable model. We present the first exact analyticexpressions for the general Drude weights in the Hubbard model, and explain howto reconcile different approaches for computing Drude weights from the previousliterature.

Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach