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

Johannes Feldmeier^1,2, Pablo Sala^1,2, Giuseppe De Tomasi³

¹Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.

Physical Review Letters

|January 7, 2021

Summary

Systems conserving dipole or higher-moment charges exhibit subdiffusive decay, unlike typical diffusive transport. This study analytically models these anomalous exponents, revealing distinct scaling behaviors for conserved moments.

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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.