Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Non-equilibrium systems

Background:

• Global conserved quantities typically cause diffusive transport in interacting systems at late times.
• Understanding deviations from diffusive behavior is crucial for characterizing complex physical systems.

Purpose of the Study:

• To investigate the transport dynamics in systems with conserved dipole moments and higher-moment generalizations.
• To determine if higher-moment conservation alters the typical diffusive transport scenario.

Main Methods:

• Modeling system evolution using cellular automata for dipole and quadrupole conservation.
• Developing a general analytical hydrodynamic model for higher-moment conservation.
• Numerically calculating anomalous exponents and analyzing charge correlation functions.

Main Results:

• Systems conserving dipole or higher-moment charges display subdiffusive decay, deviating from standard diffusive transport.
• Distinct anomalous exponents were found for dipole and quadrupole conservation.
• The hydrodynamic model accurately describes the scaling form of charge correlation functions.

Conclusions:

• Higher-moment conservation provides a mechanism to escape diffusive transport, leading to subdiffusive behavior.
• The number of conserved moments dictates the anomalous scaling exponents.
• Experimental signatures for higher-moment conservation warrant further investigation.