Related papers: Generalized one-dimensional nonpolynomial Schr\"od…
We investigate the cross-over from three to one dimension in a Bose gas confined in highly anisotropic traps. By using Quantum Monte-Carlo techniques, we solve the many-body Schrodinger equation for the ground state and obtain exact results…
We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical…
We have measured the damped motion of a trapped Bose-Einstein condensate, oscillating with respect to a thermal cloud. The cigar-shaped trapping potential provides enough transverse confinement that the dynamics of the system are…
The Gross-Pitaevskii (GP) or nonlinear Schr\"odinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possess a modified Schr\"odinger symmetry in two spatial dimensions, in the presence of a harmonic trapping…
Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein…
Within a variational approach to solve the Gross-Pitaevskii equation we investigate dynamical properties of a rotating Bose-Einstein condensate which is confined in an anharmonic trap. In particular, we calculate the eigenfrequencies of…
The mean-field dynamics of a Bose-Einstein condensate is studied in presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be…
We investigate the dynamical behavior of the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A…
Here we describe a weakly interacting Bose gas on a curved manifold, which is embedded in the three-dimensional Euclidean space.~To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the…
We study the mean-field dynamics and the reduced-dimension character of two-mode Bose-Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of…
We consider the evolution of $N$ bosons interacting with a repulsive short range pair potential in three dimensions. The potential is scaled according to the Gross-Pitaevskii scaling, i.e. it is given by $N^2V(N(x_i-x_j))$. We monitor the…
We propose an alternative implementation of the Projected Gross-Pitaevskki equation adapted for numerical modeling of the atomic Bose-Einstein condensate trapped in a toroidally-shaped potential. We present an accurate and efficient scheme…
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the…
We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the…
We consider a gas of $N$ bosons in a box with volume one interacting through a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently small, we show that…
We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated…
We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in…
We present a theory for the description of energy relaxation in a nonequilibrium condensate of bosonic particles. The approach is based on coupling to a thermal bath of other particles (e.g., phonons in a crystal, or noncondensed atoms in a…
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 investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection to the entanglement between its spatial degrees of freedom. We argue that the reduced-dimensionality of the BEC is physically…