Self-similar inverse cascade from generalized symmetries

Abstract

We investigate the role of generalized symmetries in driving non-equilibrium and non-linear phenomena, specifically focusing on turbulent systems. While conventional turbulence studies have revealed inverse cascades driven by conserved quantities integrated over the entire space, such as helicity in three spatial dimensions, the influence of higher-form symmetries, whose conserved charges are defined by integration over subspaces, remains largely unexplored. We demonstrate a novel mechanism where higher-form symmetries naturally induce a self-similar inverse cascade. Taking axion electrodynamics with non-linear topological interaction as a paradigmatic example, we show that the conserved charge associated with its 1-form symmetry drives the system toward large-scale coherent structures through a universal scaling behavior characterized by analytically determined scaling exponents. Our findings suggest that higher-form symmetries can provide a fundamental organizing principle for understanding non-equilibrium phenomena and the emergence of coherent structures in turbulent systems.

Figures (3)

• Figure 1: Spectral functions for energy and topological charge at different times. Both spectral functions exhibit the inverse cascade.
• Figure 2: Rescaled spectral functions for energy and topological charge at different times according to the scaling laws \ref{['eq:exponents']}--\ref{['eq:gscaling']}. Both rescaled spectral functions converge at later times, indicating self-similarity.
• Figure 3: Time evolution of $N_{\rm kin}$ (red), $N_{\rm top}$ (green), and $\xi^{-1}$ (blue). Black dashed line illustrates $t^{-1/2}$ asymptotic behavior of $N_{\rm kin}$ and $\xi^{-1}$.