Hydrodynamic fluctuations in relativistic superfluids

The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant relativistic theory previously suggested by Khalatnikov, Lebedev, and Carter, and some potentials in this theory are given explicitly. We discuss hydrodynamic fluctuations in the presence of dissipative effects, and we derive the corresponding set of hydrodynamic correlation functions. Kubo relations for the transport coefficients are obtained.