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JETP Letters

, Volume 106, Issue 4, pp 223–228 | Cite as

Parametric instability of oscillations of a vortex ring in a z-periodic Bose condensate and return to the initial state

  • V. P. Ruban
Condensed Matter

Abstract

The dynamics of deformations of a quantum vortex ring in a Bose condensate with the periodic equilibrium density ρ(z) = 1 − ϵ cos z has been considered in the local induction approximation. Parametric instabilities of normal modes with the azimuthal numbers ±m at the energy integral E near the values \(E_m^{\left( p \right)} = 2m\sqrt {{m^2} - 1} /p\), where p is the order of resonance, have been revealed. Numerical experiments have shown that the amplitude of unstable modes with m = 2 and p = 1 can sharply increase already at ϵ ~ 0.03 to values about unity. Then, after several fast oscillations, fast return to a weakly perturbed state occurs. Such a behavior corresponds to the integrable Hamiltonian Hσ(E 2 (1) E)(|b +|2 + |b -|2)-ϵ(b + b - + b +*b -*)+u(|b +|4 + |b -|4)+w|b +|2|b -|2 for two complex envelopes b ±(t). The results have been compared to parametric instabilities of the vortex ring in the condensate with the density ρ(z, r) = 1 − r 2 − αz 2, which occur at α ≈ 8/5 and 16/7.

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Copyright information

© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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