The evolution of a quantum vortices system: the spatio-temporal scale
hierarchy and the turbulence in the critical mode
- URL: http://arxiv.org/abs/2309.01085v1
- Date: Sun, 3 Sep 2023 05:39:13 GMT
- Title: The evolution of a quantum vortices system: the spatio-temporal scale
hierarchy and the turbulence in the critical mode
- Authors: Talalov S.V
- Abstract summary: We consider the small variations of the ring-shaped loops only, which include both helical-type shape variations and small excitations of the flow in the vortex core.
The specific type of these loops interaction is chosen in way that the constructed theory can serve as the model of turbulent flow at the critical mode.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This paper investigates the evolution and interaction of the quantum vortex
loops with the small radius of the core $a$. The quantization scheme of the
classical vortex system is based on the approach proposed by the author
earlier.
We consider the small variations of the ring-shaped loops only, which include
both helical-type shape variations and small excitations of the flow in the
vortex core. The quantization of both an initial radius of the vortex ring $R$
and the circulation $\Gamma$ is deduced from the quantum theory first
principles but is not postulated separately. The constructed model leads to the
appearance of a spatio-temporal scale hierarchy in the quantum description of
the vortices. The method of random Hamiltonians is used to describe the
interaction of vortex loops. The specific type of these loops interaction is
chosen in way that the constructed theory can serve as the model of turbulent
flow at the critical mode.
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