- Slippage and Boundary Layer Probed in an Almost Ideal Gas by a Nanomechanical Oscillator

M. Defoort et al., Phys. Rev. Lett.**113**, 136101 (2014) - Evidence for the role of normal-state electrons in nanoelectromechanical damping mechanisms at very low temperatures

K.J. Lulla et al., Phys. Rev. Lett.**110**, 177206 (2013) - Phase Diagram of the Topological Superfluid
^{3}He Confined in a Nanoscale Slab Geometry

L.V. Levitin et al., Science**340**, 841-844 (2013) - Energy and angular momentum balance in wall-bounded quantum turbulence at very low temperatures

J.J. Hosio et al., Nature Commun.**4**, 1614 (2013) - Evidence for Helical Nuclear Spin Order in GaAs Quantum Wires

C.P. Scheller et al., Phys. Rev. Lett.**112**, 066801 (2013) - Observation of a roton collective mode in a two-dimensional Fermi liquid

H. Godfrin et al., Nature**483**, 576 (2012) - The Josephson heat interferometer

F. Giazotto, M.J. Martinez-Perez, Nature**492**, 401 (2012)

## Interaction of Kelvin waves and non-locality of the energy transfer in superfluids

*Jason Laurie, Victor S. L’vov, Sergey Nazarenko and Oleksii Rudenko*

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a *local nonlinear* (partial differential) *equation*. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

*Phys. Rev. B*

**81**, 104526 (2010)doi:

*10.1103/PhysRevB.81.104526*