Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]

TL;DR

This paper critically examines and disputes previous theories on Kelvin wave turbulence in superfluid helium, clarifying the relationship between different turbulence spectra and emphasizing the importance of explicit Hamiltonian calculations.

Contribution

It provides a detailed critique of existing Kelvin wave turbulence theories, highlighting the role of explicit Hamiltonian calculations and symmetry arguments in resolving spectrum discrepancies.

Findings

Disagrees with Sonin's interpretation of Kelvin wave turbulence.

Clarifies the relation between Vinen and L'vov-Nazarenko spectra.

Emphasizes the importance of explicit Hamiltonian calculations.

Abstract

We comment on the paper by E. B. Sonin, PRB v 85, 104516 (2012) [arXiv:1201.3188], with which we find ourselves in serious disagreement. We use this option to shed light on some important issues of a theory of Kelvin wave turbulence, touched in E. B. Sonin's paper, in particular, on the relation between the Vinen spectrum of strong- and the L'vov-Nazarenko spectrum of weak-turbulence of Kelvin waves. We also discuss the role of our explicit calculation of the Kelvin wave interaction Hamiltonian and of the "symmetry arguments" that are supposed to resolve a contradiction between the Kozik-Svistunov and L'vov-Nazarenko spectrum of weak turbulence of Kelvin waves.