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Self-Similar Inverse Cascade from Generalized Symmetries.

Yuji Hirono1,2, Kohei Kamada3,4,5, Naoki Yamamoto6

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Summary
This summary is machine-generated.

Generalized symmetries, particularly higher-form symmetries, drive inverse cascades in turbulent systems. This research reveals their role in forming large-scale coherent structures through universal scaling behavior.

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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.