Related papers: Improved low-dimensional wave equations for cigar-…
The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys.…
We study Bose-Einstein condensation in a harmonic trap with a dimple potential. We specifically consider the case of a tight and deep dimple potential which is modelled by a Dirac delta function. This allows for simpler, explicit numerical…
We develop a general formalism applying to Newtonian self-gravitating Bose-Einstein condensates. This formalism may find application in the context of dark matter halos. We introduce a generalized Gross-Pitaevskii equation including a…
We apply a path integral variational approach to obtain analytical expressions for condensate wave functions of an ultracold, interacting trapped Bose gases. As in many recent experiments, the particles are confined in a 1D or 3D harmonic…
We consider an ultracold dipolar Bose gas in a one-dimensional lattice. For a sufficiently large lattice recoil energy, such a system becomes a series of non-overlapping Bose-Einstein condensates that interact via the long-range…
We investigate the two-dimensional modified Gross-Pitaevskii equation, accounting for the effects of atom gain/loss and a time-independent isotropic confining potential, utilizing the Hirota's bilinear method. Through an appropriate…
Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field…
We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the…
We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The…
It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross - Pitaevskii equation modelling the mean-field…
Influence of the damping on collective oscillations of a one-dimensional trapped Bose gas in the mean field regime has been studied. Using the phenomenological damping approach developed by L.P. Pitaevskii, modified variational equations…
Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $\xi_1$ and $\xi_2$ and by…
We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the…
Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the…
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit…
We construct exact stationary solutions to the one-dimensional coupled Gross-Pitaevskii equations for the two-species Bose-Einstein condensates with equal intraspecies and interspecies interaction constants. Three types of complex solutions…
We obtain analytic solutions to the Gross-Pitaevskii equation with negative scattering length in highly asymmetric traps. We find that in these traps the Bose--Einstein condensates behave like quasiparticles and do not expand when the…
We derive the time-dependent two-component Gross--Pitaevskii (GP) equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose-Einstein condensate, in the…
We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is described by a…
Open dissipative systems of quantum fluids have been well studied numerically. In view of a complementary analytical description we extend here the variational optimization method for Bose-Einstein condensates of closed systems to…