Oscillations of dark solitons in trapped Bose-Einstein condensates
arXiv:cond-mat/0503657 · doi:10.1103/PhysRevE.72.016615
Abstract
We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multi-scale expansion method in the limit when the potential trap is flat. The first-order approximation predicts a uniform frequency of oscillations for the dark soliton of arbitrary amplitude. The second-order approximation predicts the nonlinear growth rate of the oscillation amplitude, which results in decay of the dark soliton. The results are compared with the previous publications and numerical computations.
arXiv comment13 pages, 3 figures
References in corpus (14)
- Theory of Bose-Einstein condensation in trapped gases
- Dark Solitons in Bose-Einstein Condensates
- Watching dark solitons decay into vortex rings in a Bose-Einstein condensate
- Observation of Quantum Shock Waves Created with Ultra Compressed Slow Light Pulses in a Bose-Einstein Condensate
- Bose--Einstein solitons in highly asymmetric traps
- Motion of dark solitons in trapped Bose-Einstein condensates
- Ring Dark Solitons and Vortex Necklaces in Bose-Einstein Condensates
- Landau dynamics of a grey soliton in a trapped condensate
- Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates
- Analogies between dark solitons in atomic Bose-Einstein condensates and optical systems
- Parametric Driving of Dark Solitons in Atomic Bose-Einstein Condensates
- Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons
- Dynamical instability of a dark soliton in a quasi-one-dimensional Bose-Einstein condensate perturbed by an optical lattice
- Deformation of dark solitons in inhomogeneous Bose-Einstein condensates
Cited by in corpus (29)
- Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
- Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
- Sculpting oscillators with light within a nonlinear quantum fluid
- Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates
- Matter-wave solitons of collisionally inhomogeneous condensates
- Dark solitons as quasiparticles in trapped condensates
- Localized gap soliton trains of Bose-Einstein condensates in an optical lattice
- Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates
- Dynamics and Manipulation of Matter-Wave Solitons in Optical Superlattices
- Fluctuating and dissipative dynamics of dark solitons in quasi-condensates
- Probing quasi-integrability of the Gross-Pitaevskii equation in a harmonic-oscillator potential
- Dark solitons generation and their instability dynamics in two dimensional condensates
- Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions
- Dark solitons dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential
- Generating, dragging and releasing dark solitons in elongated Bose-Einstein condensates
- Matter-wave dark solitons in box-like traps
- Solitons Riding on Solitons: Hypersolitons and the Quantum Newton's Cradle
- Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials
- Fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates
- Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates
- Anomalous oscillations of dark solitons in trapped dipolar condensates
- Quasi-one-dimensional harmonically trapped quantum droplets
- Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential
- Long-range sound-mediated dark soliton interactions in trapped atomic condensates
- Dark Soliton Scattering in Symmetric and Asymmetric Double Potential Barriers
- Trapping wave fields in an expulsive potential by means of linear coupling
- Eigenvalues of a nonlinear ground state in the Thomas-Fermi approximation
- Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps
- Multiple fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates