Hydrodynamics of dipole-conserving fluids.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Fluid Dynamics

Background:

• Dipole-conserving fluids exhibit exotic behaviors like glassy dynamics and subdiffusive transport.
• These systems, characterized by symmetry, have lacked a complete macroscopic hydrodynamic formulation.
• Understanding these constrained systems is crucial for fields like fracton phases and glasses.

Purpose of the Study:

• To construct a consistent hydrodynamic description for dipole-conserving fluids.
• To formulate a thermodynamic theory using symmetry principles for equilibrium states.
• To investigate dissipative effects using irreversible thermodynamics.

Main Methods:

• Formulating a hydrodynamic theory based on translation, rotation, and dipole shift symmetries.
• Applying equilibrium thermodynamics and irreversible thermodynamics.
• Analyzing the impact of energy conservation on system dynamics.

Main Results:

• A consistent hydrodynamic description for dipole-conserving fluids was successfully constructed.
• Inclusion of energy conservation leads to diffusive longitudinal modes, not subdiffusive.
• Diffusion was observed at the lowest order in the derivative expansion.

Conclusions:

• This work provides a framework for describing systems with constrained dynamics.
• The findings offer a path towards understanding fracton phases and glassy matter.
• The hydrodynamic theory advances the study of exotic condensed matter systems.