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Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the…

We study the effect of lower dimensional geometry on the frequencies of the collective oscillations of a Bose-Einstein condensate confined in a trap. To study the effect of two dimensional geometry we consider a pancake-shaped condensate…

We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects…

Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…

Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas…

Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the s-wave scattering lengths are comparable to the mixture…

The shift in condensation temperature caused by interactions is studied up to second order in the s-wave scattering length in a Bose-Einstein condensate trapped in a temperature-dependent three-dimensional generic potential. With no…

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the…

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions…

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1/r$ interaction, we point out that the instance of self-trapping of the condensate, without external trap…

The effect of dipolar orientation with respect to the condensate plane on the mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped confinement is discussed. The stability of a quasi-two-dimensional condensate, with…

We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution of the…

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semi-quantitative analysis we find the size, shape and excitation energy as a…

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function psi(x,y) is a Gaussian exp(-r^2/2),…

We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the…

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment…

The thermally induced coherent collapse of Bose-Einstein condensates at finite temperature is the dominant decay mechanism near the critical scattering length in condensates with at least partially attractive interaction. The collapse…

The dynamics of a 2D Bose-Einstein condensate in optical trap is studied taking into consideration fluctuations of the far-off-resonance laser field intensity. The problem is described in the frame of the mean field Gross-Pitaevskii…

The dimensionality of a system profoundly influences its physical behaviour, leading to the emergence of different states of matter in many-body quantum systems. In lower dimensions, fluctuations increase and lead to the suppression of…

A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed…