Hydrodynamic fluctuations in relativistic superfluids

TL;DR

This paper develops a Hamiltonian framework for relativistic superfluids, explores hydrodynamic fluctuations with dissipation, and derives correlation functions and Kubo relations for transport coefficients.

Contribution

It provides a detailed Hamiltonian formulation of relativistic superfluids and explicitly derives hydrodynamic correlation functions and transport relations.

Findings

Covariant relativistic superfluid theory derived

Hydrodynamic correlation functions obtained

Kubo relations for transport coefficients established

Abstract

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.