Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and dynamical analysis of a single vortex ring in anisotropic
  harmonically trapped three-dimensional Bose-Einstein condensates   In the present work, motivated by numerous recent experimental developments
we revisit the dynamics of a single vortex ring in anisotropic harmonic traps.
At the theoretical level, we start from a general Lagrangian dynamically
capturing the evolution of a vortex ring and not only consider its spectrum of
linearized excitations, but also explore the full nonlinear dynamical evolution
of the ring as a vortical filament. The theory predicts that the ring is stable
for $1 \leq \lambda \leq 2$, where $\lambda=\omega_z/\omega_r$ is the ratio of
the trapping frequencies along the $z$ and $r$ axes, i.e., for spherical to
slightly oblate condensates. We compare this prediction with direct numerical
simulations of the full 3D Gross-Pitaevskii equation (GPE) capturing the
linearization spectrum of the ring for different values of the chemical
potential and as a function of the anisotropy parameter $\lambda$. We identify
this result as being only asymptotically valid as the chemical potential $\mu
\rightarrow \infty$, revealing how the stability interval narrows and, in
particular, its upper bound decreases for finite $\mu$. Finally, we compare at
the dynamical level the results of the GPE with the ones effectively capturing
the ring dynamics, revealing the unstable evolution for different values of
$\lambda$, as well as the good agreement between the two.

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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex