Comment on "Reconnection of quantized vortex filaments and the Kolmogorov spectrum"

TL;DR

This comment clarifies that the Kolmogorov spectrum in superfluids is unlikely to originate from vortex reconnections, as previous calculations overlooked the dominant self-energy term which influences the energy spectrum.

Contribution

It highlights the importance of including the self-energy term in analyzing the energy spectrum, challenging prior claims linking reconnections to the Kolmogorov spectrum.

Findings

Self-energy dominates the kinetic energy spectrum.

Reconnection events alone do not produce the Kolmogorov spectrum.

The $1/k$ spectrum from self-energy is more significant.

Abstract

In this Comment we would like to emphasize that in Phys. Rev. B 90, 104506 (2014) the calculated energy spectrum takes into account only the small interaction (cross) term and, additionally, this term is only calculated at the instant when the two vortices reconnect. The majority of the kinetic energy is contained in the self-energy term which has a characteristic spectrum of $1/k$. If this, and the additional average over time, is taken into account the suggested Kolmogorov type $k^{-5/3}$ spectrum is likely not visible in the kinetic energy spectrum which contains both terms. Therefore, we find the suggestion misleading that the Kolmogorov spectrum in superfluids arises from the reconnection of vortices.