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

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.