Abstract
The nonlinear dynamics of self-bound Bose–Einstein matter waves under the action of an attractive nonlocal and a repulsive local interaction is analyzed by means of a time-dependent variational formalism. The mean-field model described by the Gross–Pitaevskii equation (GPE) is reduced to a single second-order conservative ordinary differential equation admitting a potential function. The stable fixed points and the linear oscillation frequencies of the breather modes are determined. The chosen nonlocal interactions are a Gaussian-shaped potential and a van der Waals-like potential. The variational solutions are compared with direct numerical simulations of the GPE, for each of these nonlocalities. The spatio-temporal frequency spectra of linear waves are also determined.
Highlights
In many situations, nonlocal spatial interactions play a central role
The experimental observations of dipolar Bose–Einstein condensates (BECs) in systems composed of atoms with a large magnetic moment provided a breakthrough in ultra-cold gas physics [1,2,3]
The nonlinear dynamics of a completely selfbound BEC with nonlocal coupling has been analyzed by means of a time-dependent variational formalism
Summary
Nonlocal spatial interactions play a central role. In particular, the experimental observations of dipolar Bose–Einstein condensates (BECs) in systems composed of atoms with a large magnetic moment provided a breakthrough in ultra-cold gas physics [1,2,3]. Proposals include the self-trapping of mesoscopic atomic clouds by a collective excitation of Rydberg atom pairs [5], additional interactions in dilute BECs of alkali atoms besides the dipolar interaction, creating 2D BEC solitons [6], the role of the orbital angular momentum on the arrest of collapse of vortexfree elliptical clouds of BECs described by Ermakov systems [7, 8], and the manipulation of the atomic scattering length.
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