We review the theory of relaxational kinetics of superfluid turbulence--a tangle of quantized vortex lines--in the limit of very low temperatures when the motion of vortices is conservative. While certain important aspects of the decay depend on whether the tangle is non-structured, like the one in the Kibble-Zurek picture, or essentially polarized, like the one that emulates the Richardson-Kolmogorov regime of classical turbulence, there are common fundamental features. In both cases, there exists an asymptotic range in the wavenumber space where the energy flux is supported by the cascade of Kelvin waves (kelvons)--precessing distortions propagating along the vortex filaments. At large enough wavenumbers, the Kelvin-wave cascade is supported by three-kelvon elastic scattering. At T=0 the dissipative cutoff of the Kelvin-wave cascade is due to the emission of phonons, in which an elementary process converts two kelvons with almost opposite momenta into one bulk phonon. Along with the standard set of conservation laws, a crucial role in the theory is played by the fact of integrability of the local induction approximation (LIA) controlled by the parameter Λ= \ln (λ/a_0), with λthe characteristic kelvon wavelength and a_0 the vortex core radius. While excluding a straightforward onset of the pure three-kelvon cascade, the integrability of LIA does not plug the cascade because of the availability of the kinetic channels associated with vortex line reconnections. We argue that the crossover from Richardson-Kolmogorov to the Kelvin-wave cascade is due to eventual dominance of local induction of a single line over the collective induction of polarized eddies, which causes the breakdown of classical-fluid regime and gives rise to a reconnection-driven inertial range.
Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]
本文对E. B. Sonin，PRB v 85，104516（2012）[arXiv：1201.3188]，我们发现自己严重不同意。我们用这个选项来阐明开尔文波湍流理论的一些重要问题，在E。B. Sonin的论文，特别是，在强的Vinen谱和L 'vov-Nazarenko谱的弱湍流的开尔文波之间的关系。我们还讨论了我们的明确计算的开尔文波相互作用的哈密顿量和“对称性参数”，应该解决之间的矛盾的Kozik-Svistunov和L 'vov-Nazarenko谱的弱湍流的开尔文波的作用。
Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas
在二维和三维空间中分析了远离热平衡的稀薄简并玻色气体动力学的非热不动点。详细研究了以前在非微扰量子场论方法中发现的、最近被证明与涡旋动力学和超流湍流有关的普适幂律分布[Phys. Rev. B 84，020506（R）（2011）]。结果意味着解释的标度行为的独立涡激发的超流体和拓扑激发的统计可以描述的波动湍流的框架。发现在单粒子动量分布中观察到的特定标度指数与不可逆性以及波相互作用所遵守的守恒定律是一致的。此外，长波长的声学激励的涡旋轴承冷凝物，驱动的涡旋湮灭，发现遵循非热幂律。在统计模式中考虑涡的相关性，长时间偏离非热不动点与涡-反涡配对有关。所研究的非热不动点可在冷气体实验中得到。这些结果揭示了超流湍流的基本方面，并对相关现象具有很强的潜在影响，例如，在早期宇宙膨胀或夸克-胶子等离子体动力学中。
