Hydrodynamics of ideal fracton fluids

TL;DR

This paper develops a new hydrodynamic framework for fracton fluids, deriving equations from conservation laws and analyzing fluctuations, which advances understanding of topological defect dynamics in many-body systems.

Contribution

It introduces a systematic Poisson bracket approach to derive hydrodynamics for scalar theories with fracton excitations, covering multiple classes of models.

Findings

Derived hydrodynamic equations from conservation laws for fracton theories

Analyzed hydrodynamic fluctuations and dispersion relations

Provided models for disclinations and dislocations in fracton systems

Abstract

Low-energy dynamics of many-body fracton excitations necessary to describe topological defects should be governed by a novel type of hydrodynamic theory. We use a Poisson bracket approach to systematically derive hydrodynamic equations from conservation laws of scalar theories with fracton excitations. We study three classes of theories. In the first class we introduce a general action for a scalar with a shift symmetry linear in the spatial coordinates, whereas the second one correspond with a complex scalar, while the third class serves as a toy model for disclinations and dislocations propagating along the Burgers vector. We apply our construction to study hydrodynamic fluctuations around equilibrium states and derive the dispersion relations of hydrodynamic modes.