Critical Dynamics of Superfluids

TL;DR

This work develops a relativistic effective field theory for the nearly critical dynamics of superfluids, integrating the order parameter with standard hydrodynamics and detailing both dissipative and fluctuation effects. It identifies an extra, nonredundant term (Zπ) in the order-parameter dynamics that is required to match holographic (mean-field) predictions, and it provides a Keldysh-Schwinger derivation to incorporate fluctuations consistently. In the asymptotic limits, the theory reproduces conventional superfluid hydrodynamics in the infrared and charged normal-fluid hydrodynamics in the ultraviolet, while revealing critical-point signatures such as divergent bulk viscosities and a gapped amplitude (Higgs) mode with its own diffusion. The results, together with holographic checks, advance the understanding of critical dynamics in superfluids and offer a framework to study fluctuations via the Keldysh-Schwinger formalism and beyond mean-field theory.

Abstract

We use standard techniques of hydrodynamics to construct a relativistic effective field theory for the low energy dynamics of nearly critical superfluids. In an appropriate non-relativistic limit, our theory predicts an additional coefficient when compared and contrasted to earlier work of Khalatnikov and Lebedev. In addition, we provide an alternative derivation of the same effective theory, using the Keldysh-Schwinger framework for non-equilibrium systems. Finally, we comment on the comparison with the results of an appropriate holographic computation presented in a companion paper. This provides further evidence in support of the theory we propose and confirms the existence of the extra coefficient we identified.