相关论文: Localization phenomena in Nonlinear Schrodinger eq…
We study the properties of the ground state of Bose-Einstein condensates with spatially inhomogeneous interactions and show that the atom density experiences a strong localization at the spatial region where the scattering length is close…
We study the effect of nonlocality on the collapse properties of a self-focusing Nonlinear Schr\"odinger system related to Bose-Einstein condensation problems. Using a combination of moment techniques, time dependent variational methods and…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
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…
Ground state properties of trapped Bose condensate with repulsive interaction in non-homogeneous gravitational field are studied. Spatial structure of Bose condensate and its momentum distributions in 3-D anisotropic trap are considered by…
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or…
We consider time-dependent nonlinear Schroedinger equations subject to smooth, lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale. After an appropriate scaling we study the homogenization…
The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schrodinger equation with a finite square well potential, which models a Bose-Einstein condensate in a quasi-one-dimensional…
It is shown that the quasi-one-dimensional Bose-Einstein condensate is experimentally accessible and rich in intriguing phenomena. We demonstrate numerically and analytically the existence, stability, and perturbation-induced dynamics of…
By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive…
Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the…
It is shown that inhomogeneous nonlinear interactions in a Bose-Einstein condensate loaded in an optical lattice can result in delocalizing transition in one dimension, what sharply contrasts to the known behavior of discrete and periodic…
We use a change of variables that turns the critical nonlinear Schroedinger equation into the critical nonlinear Schroedinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on…
Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schr\"odinger equation with a finite square-well potential for a range of…
We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii…
In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose-Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutativity on energy spectrum of the condensate.…
All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the…
We show how the chiral properties of Bose Einstein condensates subject to current-density interactions and loaded in optical lattices can be observed in the realization of nonlinear Bloch states, whose spectrum lacks the usual periodic…
The motto of this paper is: Let's face Bose-Einstein condensation through nonlinear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose-Einstein condensates…