Approximate symmetries, pseudo-Goldstones, and the second law of thermodynamics

TL;DR

This paper develops a hydrodynamic framework for systems with approximate symmetries, revealing universal relations between damping and diffusion of pseudo-Goldstones and uncovering new effects related to explicit symmetry breaking.

Contribution

It introduces a general hydrodynamic approach for systems with approximate symmetries, connecting thermodynamics to pseudo-Goldstone dynamics and exploring applications to condensed matter systems.

Findings

Derived universal relation between damping and diffusion of pseudo-Goldstones

Identified new physical effects due to explicit symmetry breaking

Applied framework to pinned superfluids and charge density waves

Abstract

We propose a general hydrodynamic framework for systems with spontaneously broken approximate symmetries. The second law of thermodynamics naturally results in relaxation in the hydrodynamic equations, and enables us to derive a universal relation between damping and diffusion of pseudo- Goldstones. We discover entirely new physical effects sensitive to explicitly broken symmetries. We focus on systems with approximate U(1) and translation symmetries, with direct applications to pinned superfluids and charge density waves. We also comment on the implications for chiral perturbation theory.