Related papers: Stability of the homogeneous Bose-Einstein condens…
We review recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective field theory methods are used to formulate a systematic perturbative framework that can be used to…
In this paper we investigate the stability of a recently introduced Bose-Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employed to derive equations of motion for…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
We study the Bose-Einstein condensation (BEC) for a system of $^7Li$ atoms, which have negative scattering length (attractive interaction), confined in a harmonic potential. Within the Bogoliubov and Popov approximations, we numerically…
We study Bose gases in $d$ dimensions, $d \ge 2$, with short-range repulsive pair interactions, at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus…
Major issues arising in the theory of Bose-Einstein condensation are reviewed. These issues, although being principally important, are very often misunderstood, which results in wrong conclusions. The basic point is global gauge symmetry…
Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit…
In this work we numerically explore the quantum behavior of a classically unstable relativistic Bose-Einstein condensate (BEC). The main goal is to study the phenomenon of so-called quantum break time which amounts to a significant…
We study the interference effects between three weakly linked trapped Bose-Einstein condensates (BEC) as a generalization of the two-component condensates. Three coupled Gross-Pitaevskii equations (GPE) are used to describe the dynamics of…
We consider the restriction placed by the Bogoliubov inequality on the nature of the Bose-Einstein condensates (BECs) for interacting atoms in a spatial dimension D </- 2 and in the presence of an external arbitrary potential, which may be…
We study the pairing instability and mechanical collapse of a dilute homogeneous bose gas with an attractive interaction. The pairing phase is found to be a saddle point, unstable against pairing fluctuations. This pairing saddle point…
We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths…
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show that in the trace topology of one-body…
We study the stability of a quasi-one-dimensional dipolar Bose-Einstein condensate (dBEC) that is perturbed by a weak lattice potential along its axis. Our numerical simulations demonstrate that systems exhibiting a roton-maxon structure…
The mean-field properties of finite-temperature Bose-Einstein gases confined in spherically symmetric harmonic traps are surveyed numerically. The solutions of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for the…
Bose-Einstein condensation in a Bose gas is studied analytically, in any positive dimensionality ($d>0$) for identical bosons with any energy-momentum positive-exponent ($s>0$) plus an energy gap $\Delta$ between the ground state energy…
The central problem of this chapter is temporal coherence of a three-dimensional spatially homogeneous Bose-condensed gas, initially prepared at finite temperature and then evolving as an isolated interacting system. A first theoretical…
The motion of single quantum particle through Bose-Einstein condensate (BEC) is considered within perturbation theory with respect to the particle-BEC interaction. The Hamiltonian of BEC is diagonalized by means of Bogoliubov's method. The…
In the framework of the O(N) three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the 1/N expansion to evaluate, within the large N limit, the parameter r_c which is directly related to…
Despite the long history of the theory of Bose-Einstein condensation, there exist till nowadays some slippery points that are often misunderstood and result in confusion. The report touches some of these points, explaining the following:…