Abstract
One of the main features of superfluids is the presence of topological defects with quantised circulation. These objects are known as quantum vortices and exhibit a hydrodynamic behaviour. Nowadays, particles are the main experimental tool used to visualise quantum vortices and to study their dynamics. We use a self-consistent model based on the three-dimensional Gross-Pitaevskii (GP) equation to explore theoretically and numerically the attractive interaction between particles and quantized vortices at very low temperature. Particles are described as localised potentials depleting the superfluid and following Newtonian dynamics. We are able to derive analytically a reduced central-force model that only depends on the classical degrees of freedom of the particle. Such model is found to be consistent with the GP simulations. We then generalised the model to include deformations of the vortex filament. The resulting long-range mutual interaction qualitatively reproduces the observed generation of a cusp on the vortex filament during the particle approach. Moreover, we show that particles can excite Kelvin waves on the vortex filament through a resonance mechanism even if they are still far from it.
Highlights
Quantum vortices have a long history in physics of superfluids and superconductors
We have studied the interaction of a particle and a quantum vortex in a self-consistent framework given by the particle-superfluid Hamiltonian [1]
The superfluid is described by the Gross-Pitaevskii equation and the particle through classical degrees of freedom
Summary
Quantum vortices have a long history in physics of superfluids and superconductors. Already in the 40’s Onsager had suggested the existence of quantised flows. An important experimental breakthrough occurred in 20065, when quantum vortices were directly visualised by using micrometer-sized hydrogen particles These impurities are trapped inside the vortex core and they can be directly visualised by using standard particle-tracking techniques, that are commonly exploited in classical hydrodynamic turbulence. Its equations of motion have been generalised to the case where the flow is prescribed by the two-fluid model15,16 This model provides a large-scale description of a finite temperature superfluid where vortices are described with a coarse-grained field, the quantised nature of superfluid vortices is missing. A different model that does account for the quantised nature of superfluid vortices, was introduced by Schwartz and it is known as the vortex filament method17 In this case, the dynamics of particles has been addressed both theoretically and numerically. The consequences of the long-range interaction between the particle and the filament are analytically studied and a prediction for the generation of Kelvin wave is obtained
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