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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 consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a hard wall trap or a harmonic oscillator trap with a tunable $\delta$-function barrier at the trap center. The mixture consists of 1D Bose gas with…
We construct a fully self-consistent non-equilibrium theory for the dynamics of two interacting finite-temperature atomic Bose-Einstein condensates. The condensates are described by dissipative Gross-Pitaevskii equations, coupled to quantum…
We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative…
We investigate the properties of a degenerate dilute gas of neutral fermionic particles in a harmonic trap that interact via dipole-dipole forces. We employ the semiclassical Thomas-Fermi method and discuss the Dirac correction to the…
This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the…
The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for…
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…
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…
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two dimensional geometry. The quantum particles have short-range, s-wave interactions described by a hard-sphere potential…
Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the…
We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational…
We perform a variational quantum Monte Carlo simulation of an interacting Fermi gas confined in a three dimensional harmonic potential. This gas is considered as the precursor system from which a molecular bosonic gas is formed. Based on…
The boson-fermion atomic bound states (composite fermion) and their roles for the phase structures are studied in a bose-fermi mixed condensate of atomic gas in finite temperature and density. The two-body scattering equation is formulated…
The thermodynamical properties of interacting Bose atoms in a harmonic potential are studied within the mean-field approximation. For weak interactions, the quantum statistics is equivalent to an ideal gas in an effective mean-field…
We consider non centered vortices and their arrays in a cylindrically trapped Bose-Einstein condensate at zero temperature. We study the kinetic energy and the angular momentum per particle in the Thomas Fermi regime and their dependence on…
The phase structures of the boson-fermion (B and F) mixed condensates of atomic gas are discussed under the existence of boson-fermion composite fermions (quasi-bound states) BF from the equilibrium in B+F -> BF. Especially we discuss the…
We study the thermodynamic behaviour of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin…
We present the theory of damping of low-energy excitations of a trapped Bose condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of…
We provide a description of the dynamic structure factor of a homogeneous unitary Fermi gas at low momentum and low frequency, based on the dissipative two-fluid hydrodynamic theory. The viscous relaxation time is estimated and is used to…