A theory for non-Abelian superfluid dynamics

TL;DR

This paper develops a theoretical framework for non-Abelian superfluids with partially broken symmetry, deriving transport equations and the Josephson relation using an offshell hydrodynamic formalism.

Contribution

It introduces a novel formalism for non-Abelian superfluid dynamics, including a new parametrization of hydrodynamic transport and derivation of the Josephson equation.

Findings

Derived superfluid transport equations consistent with the second law

Provided an alternative parametrization of hydrodynamic transport

Generalized the classification of hydrodynamic transport to superfluids

Abstract

We write down a theory for non-Abelian superfluids with a partially broken (semisimple) Lie group. We adapt the offshell formalism of hydrodynamics to superfluids and use it to comment on the superfluid transport compatible with the second law of thermodynamics. We find that the second law can be also used to derive the Josephson equation, which governs dynamics of the Goldstone modes. In the course of our analysis, we derive an alternate and mutually distinct parametrization of the recently proposed classification of hydrodynamic transport and generalize it to superfluids.