Related papers: A Levinson theorem for scattering from a Bose-Eins…
Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger…
We present a kinetic description of Bose-Einstein condensation for particle systems being out of thermal equilibrium, which may happen for gluons produced in the early stage of ultra-relativistic heavy-ion collisions. The dynamics of bosons…
We consider interacting Bose gases trapped in a box $\Lambda = [0;1]^3$ in the Gross-Pitaevskii limit. Assuming the potential to be weak enough, we establish the validity of Bogoliubov's prediction for the ground state energy and the…
We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon,…
In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state…
We derive an expression for the collective Casimir-Polder interaction of a trapped gas of condensed bosons with a plane surface through the coupling of the condensate atoms with the electromagnetic field. A systematic perturbation theory is…
An approximate many-body theory incorporating two-body correlations has been employed to calculate low-lying collective multipole frequencies in a Bose-Einstein condensate containing $A$ bosons, for different values of the interaction…
The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schr\"odinger…
From the microscopic theory, we derive a number conserving quantum kinetic equation, valid for a dilute Bose gas at any temperature, in which the binary collisions between the quasi-particles are mediated by phonon-like excitations (called…
I review recent theoretical treatments of a dilute interacting condensed Bose gas in a trap. Bogoliubov's classic results for a uniform condensate are generalized to include the effect of a trap, using the Gross-Pitaevskii formalism (for…
The linearised time dependent coupled Gross-Pitaevskii equations describing the long wavelength excitations of Bose-condensed binary mixtures are solved, in the bulk and in harmonic traps for the case where only the binary phase is present.…
A Langevin equation for the complex amplitude of a single-mode Bose-Einstein condensate is derived. The equation is first formulated phenomenologically, defining three transport parameters. It is then also derived microscopically.…
We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order $N^{-1+\kappa}$, for $\kappa>0$. Assuming that $\kappa\in (0;1/43)$, we show that low-energy states of the system…
This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…
The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting…
We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an…
An analytical insight into the symmetry breaking mechanisms underlying the transition from Josephson to self-trapping regimes in Bose-Einstein condensates is presented. We obtain expressions for the ground state properties of the system of…
The quantum instability of the mean-field theory for identical bosons is shown to be described by an appropriate Bogoliubov transformation. A connection between the quantum and classical linear stability theories is indicated. It is argued…
Bogoliubov-de Gennes (BdG) equations and the excitation spectrum of a two-component Bose-Einstein condensate (BEC) are derived with an arbitrary interaction between bosons, including long-range and short range forces. The nonconverting BEC…
We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two or three of the…