Related papers: Dynamics and stability of Bose-Einstein condensate…
The properties of the superfluid phase of ultra cold bosonic atoms loaded in a circular array are investigated in the framework of the Bose-Hubbard model and the Bogoliubov theory. We derive and solve the Gross-Pitaevskii equation of the…
Recently, Freilich et al. [Science 329, 1182 (2010)] experimentally discovered stationary states of vortex dipoles, pairs of vortices of opposite circulation, in dilute Bose-Einstein condensates. To explain their observations, we perform…
Two-dimensional (2D) fundamental soliton-soliton pairs are investigated in binary mixtures of Bose-Einstein condensates with attractive interactions between atoms of the same type. Both attractive and repulsive interactions between atoms of…
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a…
Using the explicit numerical solution of the axially-symmetric Gross-Pitaevskii equation we study the oscillation of the Bose-Einstein condensate induced by a periodic variation in the atomic scattering length $a$. When the frequency of…
We provide an approximate analytical expression of the mass-radius relation of a Newtonian self-gravitating Bose-Einstein condensate (BEC) with short-range interactions described by the Gross-Pitaevskii-Poisson system. These equations model…
We theoretically study the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii…
In this paper, we study the stability of three-dimensional Bose-Einstein condensates of finite temperatures at which both elastic and inelastic collisions are taken into account. The modeled governing Gross-Pitaevski equation reveals…
In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose-Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the…
We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with…
The stability and chaotic behaviors of Bose-Einstein condensates with two- and three-atom interactions in optical lattices are discussed with analytical and numerical methods. It is found that the steady-state relative population appears…
The nonlinear Dirac equation for Bose-Einstein condensates in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic…
Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic…
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…
The dynamical instabilities and ensuing dynamics of singly- and doubly-quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full 3D numerical simulations of the Gross-Pitaevskii equation.…
The dynamical instability of weakly interacting two-component Bose--Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues…
Bose-Einstein condensates are described in a mean-field approach by the nonlinear Gross-Pitaevskii equation and exhibit phenomena of nonlinear dynamics. The eigenstates can undergo bifurcations in such a way that two or more eigenvalues and…
The ground state of Bose-Einstein condensates with attractive particle interaction is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory…
It is shown that the one-dimensional nonlinear Schr\"odinger equation with a dissipative periodic potential, nonlinear losses and linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes…