On role of symmetries in Kelvin wave turbulence

Abstract

E.V. Kozik and B.V. Svistunov (KS) paper "Symmetries and Interaction Coefficients of Kelvin waves", arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010, contains a comment on paper "Symmetries and Interaction coefficients of Kelvin waves", V. V. Lebedev and V. S. L'vov, arXiv:1005.4575, 25 May 2010. It relies mainly on the KS text "Geometric Symmetries in Superfluid Vortex Dynamics}", arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a symmetry argument prevents linear in wavenumber infrared asymptotics of the interaction vertex and thereby implies locality of the Kelvin wave spectrum previously obtained by these authors. In the present note we reply to their arguments. We conclude that there is neither proof of locality nor any refutation of the possibility of linear asymptotic behavior of interaction vertices in the texts of KS.

References in corpus (6)

• The interaction of Kelvin waves and the non-locality of the energy transfer in superfluids
• Theory of decay of superfluid turbulence in the low-temperature limit
• Modeling Kelvin Wave Cascades in Superfluid Helium
• Symmetries and Interaction coefficients of Kelvin waves
• Geometric Symmetries in Superfluid Vortex Dynamics
• Comment on "Symmetries and Interaction Coefficients of Kelvin waves" [arXiv:1005.4575] by Lebedev and L'vov

Cited by in corpus (12)

• Vortices and turbulence in trapped atomic condensates
• Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
• Structure of quantum vortex tangle in He-4 counterflow turbulence
• Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
• Kelvin-wave turbulence in superfluids
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• The Kelvin-wave cascade in the vortex filament model
• Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence
• Kelvin waves and the decay of quantum superfluid turbulence
• Temperature suppression of Kelvin-wave turbulence in superfluids
• Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]
• Reply to Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence" [arXiv:1208.4593]