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Register a new userComment on Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades [arXiv:0905.0159] by J. Yepez, G. Vahala, L.Vahala and M. Soe
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Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the interpretation of the important numerical results obtained by the authors. A way to do this is suggested.
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We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the latter and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in $k$-space via a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and the closeness of the numerics for the higher-order DAM to the analytical predictions for the lower-order DAM .
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum $ESb{LN}(k)propto k^{-5/3}$ must replace in future theory (e.g. in finding the quantum turbulence decay rate) the previously used spectrum $ESb {KS}(k)propto k^{-7/5}$, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.
It is shown that criticism of my paper arXiv:0801.0656 Phys. Rev. Lett, vol. 101, 163202 (2008) by the authors of Comment arXiv:0810.3243v1 is wrong and that their main arguments are in contradiction with established concepts of statistical physics.
We investigate Kolmogorov wave turbulence in QCD or, in other words, we calculate the spectrum of gluons as a function of time, f_k(t), in the presence of a source which feeds in energy density in the infrared region at a constant rate. We find an early, an intermediate and a late time form for the gluon spectrum. Wave turbulence in QCD turns out to be somewhat different than the turbulence in the case of phi^4-type theories studied by Zakharov, Lvov and Falkovich. The hope is that a good understanding of QCD wave turbulence might lead to a better understanding of the instability problem in the early stages of the evolution after a heavy ion collision.
The Comment by Wolfgang Ketterle (Ref.[1]) purports to present a viable model of superradiance in condensates. However, Ref.[1] is not able to explain the red/blue pump detuning asymmetry that was first observed recently by us (Ref.[2]). It is clear from our original paper (Ref.[3]) that the rate-equation-based theories of Ref.[1] are incomplete since they only model the final growth stage of the process when a red-detuned pump is used. Our theoretical framework (Ref.[3]), on the other hand, also treats the initial growth stage of superradiance and is therefore also capable of explaining the genesis of the red/blue detuning asymmetry (Ref.[2]). This is the key message of our response, which we frame in terms of reference to the specific points raised in Ref. [1].
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