Geometric Symmetries in Superfluid Vortex Dynamics

Details Geometric Symmetries in Superfluid Vortex Dynamics Geometric Symmetries in Superfluid Vortex Dynamics

2010-06-02

arxiv.org/abs/1006.0506v2

Phys. Rev. B 82, 140510(R) (2010)

Physics

Condensed Matter

Other Condensed Matter

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

Scientific paper

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.

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