Geometric Symmetries in Superfluid Vortex Dynamics

Abstract

Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, $w(z)=x(z)+iy(z)$, describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which---apart from their rather specific expressions in terms of $w(z)$---are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines---the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wavenumber space. Similar considerations apply to other systems with purely geometric degrees of freedom.

4 REVTeX pages, minor stylistic changes, references to recent related preprints added

References in corpus (8)

• Spontaneous vortices in the formation of Bose-Einstein condensates
• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Bottleneck crossover between classical and quantum superfluid turbulence
• Quantum and quasiclassical types of superfluid turbulence
• The interaction of Kelvin waves and the non-locality of the energy transfer in superfluids
• Quantum turbulence in propagating superfluid vortex front
• Gradual eddy-wave crossover in superfluid turbulence
• Scanning Superfluid-Turbulence Cascade by Its Low-Temperature Cutoff

Cited by in corpus (12)

• Quantum hydrodynamics
• Energy Spectra of Quantum Turbulence: Large-scale Simulation and Modeling
• Structure of quantum vortex tangle in He-4 counterflow turbulence
• Kelvin-wave turbulence in superfluids
• Dynamics of quantum turbulence of different spectra
• Energy and Vorticity Spectra in Turbulent Superfluid ${}^4$He from $T=0$ to $T_{\lambda }$
• The Kelvin-wave cascade in the vortex filament model
• Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence
• Kelvin waves and the decay of quantum superfluid turbulence
• On role of symmetries in Kelvin wave turbulence
• Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T = 0 superfluid turbulence" [arXiv:1201.3188]
• Reply to Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence" [arXiv:1208.4593]