Related papers: The Nonlinear Dirac Equation in Bose-Einstein Cond…
A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in…
We study the effect of a logarithmic nonlinearity in the Schr\"odinger equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate (BEC). The logarithmic nonlinearity was one of the first proposed nonlinear extensions to…
A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the Gross-Pitaevskii equation (the nonlinear…
We consider the inner limit system describing the phase separation in two-component Bose-Einstein condensates linearized around the one-dimensional solution in an infinite strip with zero and periodic boundary conditions, and obtain optimal…
We study the nonequilibrium dynamics of a Bose-Einstein condensate which is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the…
Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for…
Quantum interferometry and quantum information processing have been proposed for Bose-Einstein condensates (BECs), but BECs are described in complicated ways such as using quantum field theory or using a nonlinear differential equation.…
In this paper, we study the bound state analysis of a one dimensional nonlinear version of the Schr\"{o}dinger equation for the harmonic oscillator potential perturbed by a $\delta$ potential, where the nonlinear term is taken to be…
A homogeneous polarized dipolar Bose-Einstein condensate is considered in the presence of weak quenched disorder within mean-field theory at zero temperature. By first solving perturbatively the underlying Gross-Pitaevskii equation and then…
In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from…
We develop theory for a flattened dipolar Bose-Einstein condensate (BEC) produced by harmonic confinement along one direction. The role of both short-ranged contact interactions and long-ranged dipole-dipole interactions (DDIs) is…
We consider a hybrid atom-optomechanical system consisting of a mechanical membrane inside an optical cavity and an atomic Bose-Einstein condensate outside the cavity. The condensate is confined in an optical lattice potential formed by a…
We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $\delta$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys…
We study theoretically the Bose-Einstein condensation in periodic polariton lattices in presence of a localized reservoir. Using the Schr\"odinger and Boltzmann equations, we find analytically the parameters determining the choice of the…
We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field…
Optical bound states in the continuum (BIC) are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone, i.e., in the…
We explore the formation and collective modes of Bose-Einstein condensate of Dirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an employed approach is general and could be used to describe Bose-Einstein condensates…
We study localized nonlinear excitations of a dilute Bose-Einstein condensate (BEC) with spin-orbit coupling in a deep optical lattice (OL). We use Wannier functions to derive a tight-binding model that includes the spin-orbit coupling…
The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices,…
We study the dynamics of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice in the limit of weak atom-atom interactions. Numerically we find that a BEC may develop a pulsating instability in which atoms nearly…