We report the effects of interaction on thermodynamic properties of a repulsive Bose-Einstein condensate confined in a harmonic trap by using the correlated potential harmonics expansion method. This many-body technique permits the use of a realistic interactomic interaction, which gives rise to the effective long-range interaction of the condensate in terms of the
s-wave scattering length. We have computed temperature (
T) dependence of the chemical potential, specific heat, condensate fraction, entropy, pressure, and the average energy per particle of a system containing a large number (
A) of
87Rb atoms in the Joint Institute for Laboratory Astrophysics (JILA) trap. The repulsion among the interacting bosons results in a small but measurable drop of condensate fraction and critical temperature (
Tc), compared to those of a noninteracting condensate. These are in agreement with the experiment. Although all thermodynamic quantities have a strong dependence on
A and to a smaller extent on the interatomic interaction, our numerical calculation appears to show that a thermodynamic quantity per particle follows a universal behavior as a function of
T/Tc. This shows the importance of
Tc for all thermodynamic properties of the condensate. As expected, for
T>Tc, these properties follow those of a trapped noncondensed Bose gas.
The analytical expressions of particle number, critical temperature, condensate fraction, total energy, specific heat and spatial distribution of particle current for rotating weakly interacting Bose gases in a harmonic trap are derived by using the local density approximation (LDA). The effects of weakly repulsive interaction on the above thermodynamics are discussed by introducing a positive scattering length. Our results completely coincide with those for the case of rotating ideal Bose gases when the weak interaction disappears.
The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose–Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T c , the total number of bosons N and the interaction V is also provided as a simple power law, T c ∝( N 2 V ) 2/3 .
We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number
N of atoms, harmonic oscillator length, deformation of the trap,
s-wave scattering length) fix its thermodynamic behavior in the large
N limit through two dimensionless scaling parameters. These are the reduced temperature
t=T/Tc0 and the ratio $\ensuremath{\eta}$ between the
T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature
Tc0 of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.
By using a mean-field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas of N atoms confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the noninteracting model with the same value of N. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived. \textcopyright{} 1996 The American Physical Society.