Quantum vortices in entanglement: a novel idea for large vortex filaments
S. V. Talalov
TL;DR
The paper introduces a quantum-mechanical framework for vortex filaments in quantum fluids, recasting large, filament-like structures as entangled superpositions of circular micro-/mesovortices under Local Induction Approximation and a centrally extended Galilei symmetry. It develops a quantization scheme that yields energy and circulation spectra for circular rings and extends it to arbitrary filament shapes through evolutes and coherent-state representations, predicting nontrivial, position-dependent circulation along filaments. A key result is a mechanism by which large loops can disassemble into finite filament fragments via flex points, accompanied by a surrounding layer of secondary vortices, offering a new lens on quantum turbulence in unbounded space. The work outlines experimental avenues in superfluid helium and proposes future theoretical development toward a full many-vortex Hamiltonian, density matrices for filament ensembles, and thermodynamic descriptions via partition functions.
Abstract
In this study, we propose a new approach to describing certain macroscopic objects that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and can be interpreted as a vortex filaments with any shape and size. The method is based on a quantization scheme for classical closed vortex filaments that was proposed by the author early \cite{Tal18,Tal22_1,Tal_Chaos25J}. The model we consider examines the instantaneous picture of the locations in space $\mathbb R_3$ of such filaments with a small, but non-zero, core diameter. Both energy and circulation of the studied filaments are calculated using the proposed approach. We demonstrate that the adopted concept leads to the emergence of secondary vortices around these investigated filament-like objects. We also study the specific mechanisms by which large vortex loops can disconnect and create the filament fragments . From our point of view, the proposed approach to describing vortex filaments within a vortex tangle can be seen as an important step toward understanding the appearance of quantum turbulence.