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arXiv:cond-mat/0508167 · Journal of Physics A Mathematical and General

Damping of vortex waves in a superfluid

H M Cataldo

Published Aug 31, 2005• 2 citations
arXivHTMLPDF

Abstract

The damping of vortex cyclotron modes is investigated within a generalized quantum theory of vortex waves. Similarly to the case of Kelvin modes, the friction coefficient turns out to be essentially unchanged under such oscillations, but it is shown to be affected by appreciable memory corrections. On the other hand, the non-equilibrium dynamics of the vortex energy, which is investigated within the framework of linear response theory, shows that its memory corrections are negligible. The vortex response is found to be of the Debye type, with a relaxation frequency whose dependence on temperature and impurity concentration reflects the complexity of the heat bath and its interaction with the vortex.

DOI
10.1088/0305-4470/38/37/001

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Damping of vortex waves in a superfluid

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The damping of vortex cyclotron modes is investigated within a generalized quantum theory of vortex waves. Similarly to the case of Kelvin modes, the friction coefficient turns out to be essentially unchanged under such oscillations, but it is shown to be affected by appreciable memory corrections. On the other hand, the non-equilibrium dynamics of the vortex energy, which is investigated within the framework of linear response theory, shows that its memory corrections are negligible. The vortex response is found to be of the Debye type, with a relaxation frequency whose dependence on temperature and impurity concentration reflects the complexity of the heat bath and its interaction with the vortex.
Abstract. The damping of vortex cyclotron modes is investigated within a generalized quantum theory of vortex waves. Similarly to the case of Kelvin modes, the friction coefficient turns out to be essentially unchanged under such oscillations, but it is shown to be affected by appreciable memory corrections. On the other hand, the nonequilibrium energetics of the vortex, which is investigated within the framework of linear response theory, shows that its memory corrections are negligible. The vortex response is found to be of the Debye type, with a relaxation frequency whose dependence on temperature and impurity concentration reflects the complexity of the heat bath and its interaction with the vortex.
In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.
Vortex dynamics in superfluids is investigated in the framework of the nonlinear Schr\"odinger equation. The natural motion of the vortex is of cyclotron type, whose frequency is found to be on the order of the phonon velocity divided by the coherence length, and may be heavily damped due to phonon radiation. Trapping foreign particles into the vortex core can reduce the cyclotron frequency and make the cyclotron motion underdamped. The density fluctuations can follow the vortex motion adiabatically within the phonon wavelength at the cyclotron frequency, which results in a further downward renormalization of the cyclotron frequency. We have also discussed applications on the dynamics of vortices in superconducting films. \textcopyright{} 1996 The American Physical Society.
Abstract The physical origin of mutual friction in quantum fluids is deeply connected to the fundamental nature of superfluidity. It stems from the interaction between the superfluid and normal components, mediated by the dynamics of quantized vortices that induce the exchange of momentum and energy. Despite the complexity of these interactions, their essential features can be effectively described by the dissipative point vortex model—an extension of classical vortex dynamics that incorporates finite-temperature dissipation. Mutual friction is parametrized by the longitudinal (dissipative) coefficient α\alphaα α and the transverse (reactive) coefficient α′\alpha 'α′ α ′ . Accurate measurement of these parameters provides critical insights into the microscopic mechanisms governing vortex motion and dissipation in quantum fluids, serving as a key benchmark for theoretical models. In this work, we employ the dissipative point vortex model to study how fluctuations in the initial conditions influence the inference of α\alphaα α and α′\alpha 'α′ α ′ from the time evolution of the vortex trajectories. Using experimentally realistic parameters, we show that fluctuations can introduce significant biases in the extracted values of the mutual friction coefficients. We compare our findings with recent experimental measurements in strongly interacting atomic superfluids. Applying this analysis to our recent experimental results allowed us to account for fluctuations in the correct determination of α\alphaα α and α′\alpha 'α′ α ′ .
Vortex waves and the onset of turbulence in 3^33He-B
In a recent experiment Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3^33He-B, that q=alpha/(1-alpha')<1, where alpha and alpha' are mutual friction parameters. The authors argued that this condition corresponds to Kelvin waves which are marginally damped, so for q>1 Kelvin waves cannot grow in amplitude and trigger vortex reconnections and turbulence. By analysing both axisymmetric and non-axisymmetric modes of oscillations of a rotating superfluid, we confirm that in the long axial wavelength limit the simple condition q=1 is indeed the crossover between damped and propagating Kelvin waves.
We investigate the damping mechanism of two transverse quadrupole oscillations in the single-vortex state of Bose-Einstein condensates using the linear response theory. It is demonstrated theoretically that the Kelvin modes as a propagation wave along a vortex line can be excited via Beliaev damping processes for only the counter-rotating quadrupole mode. We calculate the spectral weight of the density-response function within the Bogoliubov-Popov theory in a cylindrical system taking into account both Beliaev and Landau processes. Furthermore, we extend these considerations to the full 3D cigar-shaped system, which enables us to discuss the effects of the longitudinal confinement on the damping processes. These results are compared with the recent experiment on 87 Rb by Bretin et al. [Phys. Rev. Lett. 90, 100403 (2003)].