Excited states in the Thomas-Fermi limit: a variational approach

Abstract

Excited states of Bose--Einstein condensates are considered in the semi-classical (Thomas-Fermi) limit of the Gross--Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark solitons (density dips on the localized condensate) with respect to the harmonic potential and to each other is approximated using the averaged Lagrangian method. This permits a complete characterization of the equilibrium positions of the dark solitons as a function of the chemical potential parameter. It also yields an analytical handle on the oscillation frequencies of dark solitons around such equilibria. The asymptotic predictions are generalized for an arbitrary number of dark solitons and are corroborated by numerical computations for 2- and 3-soliton configurations.

20 pages, 4 figures

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Cited by in corpus (21)

• Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates
• Nonlinear modes in the harmonic PT-symmetric potential
• Multiple dark-bright solitons in atomic Bose-Einstein condensates
• Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with Deflated continuation
• Solitary waves in a quantum droplet-bearing system
• Exploring Rigidly Rotating Vortex Configurations and their Bifurcations in Atomic Bose-Einstein Condensates
• Exploring Vortex Dynamics in the Presence of Dissipation: Analytical and Numerical Results
• Dark-dark soliton breathing patterns in multi-component Bose-Einstein condensates
• Transitions From Order to Disorder in Multi-Dark and Multi-Dark-Bright Soliton Atomic Clouds
• On the Bifurcation and Stability of Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates
• Josephson tunneling of dark solitons in a double-well potential
• Quasi-one-dimensional harmonically trapped quantum droplets
• Long-range sound-mediated dark soliton interactions in trapped atomic condensates
• Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Dynamics of interacting dark soliton stripes
• Systematic vector solitary waves from their linear limits in one-dimensional $n$-component Bose-Einstein condensates
• Stationary states of a nonlinear Schrödinger lattice with a harmonic trap
• Stability of single and multiple matter-wave dark solitons in collisionally inhomogeneous Bose-Einstein condensates
• Small-amplitude nonlinear modes under the combined effect of the parabolic potential, nonlocality and $\mathcal{P}\mathcal{T}$ symmetry
• Existence, Stability and Dynamics of Harmonically Trapped One-Dimensional Multi-Component Solitary Waves: The Near-Linear Limit