Hydrodynamics of ideal fracton fluids

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 corresponds 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.

Automated summary

The study proposes a novel hydrodynamic theory to describe the low-energy dynamics of many-body fracton excitations, derived systematically using a Poisson bracket approach. Three classes of theories are studied, each representing different types of scalar theories with fracton excitations, and the construction is applied to study hydrodynamic fluctuations and derive dispersion relations of hydrodynamic modes around equilibrium states.