# A simple XY model for cascade transfer

- Date
- January 20 at 13:30 - 15:00, 2022 (JST)

- Speaker
- Mr. Tomohiro Tanogami (Graduate School of Science, Kyoto University)

- Venue
- via Zoom

- Language
- English

Cascade transfer is the phenomenon that an inviscid conserved quantity, such as energy or enstrophy, is transferred conservatively from large (small) to small (large) scales. As a consequence of this cascade transfer, the distribution of the transferred quantity obeys a universal scaling law independent of the details of large (small) scales. For example, in the energy cascade in fluid turbulence, the energy spectrum follows Kolmogorov's power law [1]. Such behavior is observed even in systems different from ordinary fluids, such as quantum fluid, elastic body, and spin systems. Here, we aim to establish the concept of a universality class for cascade transfer. As a first step toward this end, we propose a simple model representing one universality class [2]. In doing so, we regard cascade transfer as a cooperative phenomenon of unidirectional transport across scales and ask how it emerges from spatially local interactions. The constructed model is a modified XY model with amplitude fluctuations, in which the spin is regarded as the “velocity” of a turbulent field in d dimensions. We show that the model exhibits an inverse energy cascade with the non-Kolmogorov energy spectrum. We also discuss the relation to spin turbulence [3,4] and atmospheric turbulence [5].

*If you would like to participate, please contact Hidetoshi Taya.

## References

- U. Frisch, Turbulence, Cambridge university press (1995)
- T. Tanogami and S.-i. Sasa, A Simple XY Model for Cascade Transfer, (2021), arxiv: 2106.11670
- M. Tsubota, Y. Aoki, and K. Fujimoto, Spin-glass-like behavior in the spin turbulence of spinor Bose-Einstein condensates, Phys. Rev. A 88, 061601 (2013), doi: 10.1103/PhysRevA.88.061601
- J. F. Rodriguez-Nieva, Turbulent relaxation after a quench in the Heisenberg model, (2020), arxiv: 2009.11883
- G. D. Nastrom, K. S. Gage, and W. H. Jasperson, Kinetic energy spectrum of large-and mesoscale atmospheric processes, Nature volume 310, pages 36–38 (1984), doi: 10.1038/310036a0