A Simple XY Model for Cascade Transfer

Abstract

We propose a modified XY model in which cascade transfer emerges from spatially local interactions, where the spin corresponds to the "velocity" of a turbulent field. For this model, we theoretically calculate the scale-to-scale energy flux and the equal time correlation function in $d$ dimensions. The result indicates an inverse energy cascade with the non-Kolmogorov energy spectrum proportional to $k^{-3}$. We also numerically confirm the result for the cases $d=2$ and $d=3$. We thus conclude that the cascade transfer in our model represents a different universality class from standard fluid turbulence.

arXiv comment6 pages, 2 figures (+ supplemental material 3 pages, 8 figures). In ver. 2, the presentation has been revised substantially; In ver. 3, minor revisions are made

References in corpus (14)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Introduction to quantum turbulence
• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
• An update on the double cascade scenario in two-dimensional turbulence
• Turbulence-condensate interaction in two dimensions
• On The Three Point Velocity Correlation Functions in 2d Forced Turbulence
• Counterflow instability and turbulence in a spin-1 spinor Bose--Einstein condensate
• Spin turbulence with small spin magnitude in spin-1 spinor Bose-Einstein condensates
• Direct and inverse cascades of spin-wave turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates
• Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory
• Spin-glass-like behavior in the spin turbulence of spinor Bose-Einstein condensates
• Turbulent relaxation after a quench in the Heisenberg model
• One-dimensional hydrodynamic model generating a turbulent cascade
• Stochastic Shell Model: a model of anomalous scaling and non-Gaussian distribution in turbulence