Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization
arXiv:2112.04859 · doi:10.1016/j.euromechflu.2021.11.008
Abstract
This article investigates small oscillations of a vortex ring with zero thickness that evolves under the Local Induction Equation (LIE). We deduce the differential equation that describes the dynamics of these oscillations. We suggest the new approach to the Hamiltonian description of this dynamic system. This approach is based on the extension of the set of dynamical variables by adding the circulation as a dynamical variable. The constructed theory is invariant under the transformations of the Galilei group. The appearance of this group allows for a new viewpoint on the energy of a vortex filament with zero thickness. We quantize this dynamical system and calculate the spectrum of the energy and acceptable circulation values. The physical states of the theory are constructed with help of coherent states for the Heisenberg -Weyl group.
arXiv comment20 pages
References in corpus (5)
Cited by in corpus (8)
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