Self-Similar Inverse Cascade from Generalized Symmetries

Area of Science:

• Theoretical physics
• Nonlinear dynamics
• Condensed matter physics

Background:

• Turbulence research traditionally focuses on conserved quantities over entire spaces.
• The role of higher-form symmetries in driving nonequilibrium phenomena is underexplored.
• Conserved charges from higher-form symmetries are defined by integration over subspaces.

Purpose of the Study:

• To investigate the role of generalized symmetries in driving nonequilibrium and nonlinear phenomena in turbulent systems.
• To explore the influence of higher-form symmetries on inverse cascades.
• To demonstrate a novel mechanism for self-similar inverse cascades induced by higher-form symmetries.

Main Methods:

• Theoretical analysis of axion electrodynamics with nonlinear topological interaction.
• Investigating conserved charges associated with 1-form symmetry.
• Characterizing the system's behavior using universal scaling laws and analytically determined exponents.

Main Results:

• Demonstrated a novel mechanism where higher-form symmetries induce self-similar inverse cascades.
• Showcased how the conserved charge of 1-form symmetry drives the system towards large-scale coherent structures.
• Identified universal scaling behavior with analytically determined exponents.

Conclusions:

• Higher-form symmetries offer a fundamental organizing principle for understanding turbulent systems.
• These symmetries are crucial for the emergence of coherent structures in nonequilibrium phenomena.
• The findings provide new insights into the dynamics of turbulent systems beyond traditional approaches.