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Pré-Publication, Document De Travail Année : 2018

Structure and dynamics of vortices in a non-local model of superfluids

Résumé

The aim of this paper is to study the reconnection of vortices in a quantum fluid with a roton minimum, such as superfluid He-4. These reconnection events are thought to be at the origin of the emission of thermal excitations and the generation of Kelvin waves. The dynamics of a model of superfluids described by the Gross-Pitaevskii (GP) equations is investigated numerically. The originality of the present approach is the introduction of a non-local two-body interaction potential which yields the roton minimum in the dispersion relation, as evidenced by neutron scattering experiments in He-4. We begin with the calibration of the model, namely choosing a peculiar functional form of the interaction potential, under the constraint of being as close as possible to the experimental dispersion curve and, in the same time, preventing spurious local crystallization events that appear naturally in presence of a low-energy roton minimum. We then follow and track the phenomenon of reconnection starting with an initially perpendicular set of two vortices, each of them being independently a fundamental solution of the dynamics. A precise and quantitative study of various quantities characterizing the evolution of this phenomenon is proposed, that includes the evolution of statistics of several dynamical quantities of interest such as density and probability current, the vortex length, and the description in the appropriate Frenet-Serret frame of reference of a observed soliton that propagates along the cores of the vortices. The properties of this soliton are systematically compared to the predictions of the Local Induction Approximation (LIA), showing similarities and differences.

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Dates et versions

hal-01844982 , version 1 (19-07-2018)
hal-01844982 , version 2 (22-10-2019)

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Jason Reneuve, Julien Salort, Laurent Chevillard. Structure and dynamics of vortices in a non-local model of superfluids. 2018. ⟨hal-01844982v1⟩
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