Current quantization and fractal hierarchy in a driven repulsive lattice gas

Area of Science:

• Non-equilibrium statistical mechanics
• Condensed matter physics
• Complex systems

Background:

• Driven lattice gases are key models for non-equilibrium systems.
• Traditional models focus on short-range interactions, unlike many real-world systems.
• Slowly decaying interactions (e.g., dipole-dipole) are common in empirical driven systems.

Purpose of the Study:

• Investigate the non-equilibrium stationary state of driven lattice gases with slow-decayed repulsive interactions at zero temperature.
• Analyze particle current behavior concerning density and driving field.
• Identify unique collective phenomena arising from long-range interactions.

Main Methods:

• Numerical calculations of particle current.
• Analytical calculations of particle current.
• Analysis of density and driving field dependence.

Main Results:

• Observed an abrupt transition between insulating and conducting states.
• Identified current quantization into discrete phases with infinite differential resistivity.
• Discovered a fractal hierarchy of excitations linked to number theory (Farey sequences).

Conclusions:

• The competition between interaction scales drives these novel non-equilibrium phenomena.
• Crystalline states can unexpectedly melt upon increasing particle density.
• Findings highlight the importance of long-range interactions in driven systems.