On role of symmetries in Kelvin wave turbulence

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

Comment on "Symmetries and Interaction Coefficients of Kelvin waves" [arXiv:1005.4575] by Lebedev and L'vov

We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the symmetry with respect to a tilt of a quantized vortex line does not yet prohibit coupling between Kelvin waves and the large-scale slope of the line. Ironically, the counterexample of an effective scattering vertex in the local induction approximation (LIA) attempted by Lebedev and L'vov invalidates their logic all by itself being a notoriously known example of how symmetries impose stringent constraints on kelvon kinetics---not only the coupling in question but the kinetics in general are absent within LIA. We further explain that the mistake arises from confusing symmetry properties of a specific mathematical representation in terms of the canonical vortex position field w(z) = x(z) + iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of the z-axis, with those of the real physical system recovered in final expressions.Comment: comment on arXiv:1005.4575, version accepted in JLTP with minimal changes: abstract adde

Symmetries and Interaction coefficients of Kelvin waves

We considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic is not forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy

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Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; corresponding kinetic equation is derived. On the basis of the kinetic equation, we prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.Comment: 4 pages, RevTe

Diagrammatic Monte Carlo for Correlated Fermions

We show that Monte Carlo sampling of the Feynman diagrammatic series (DiagMC) can be used for tackling hard fermionic quantum many-body problems in the thermodynamic limit by presenting accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime. Sampling Feynman's diagrammatic series for the single-particle self-energy we can study moderate values of the on-site repulsion ($U/t \sim 4$) and temperatures down to $T/t=1/40$. We compare our results with high temperature series expansion and with single-site and cluster dynamical mean-field theory.Comment: 4 pages, 5 figures, stylistic change

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Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at http://www.springerlink.co

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