3 research outputs found
Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive
the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic
equations and the associated equation of motion for the condensate wavefunction
for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and
Kadanoff (KK) for a uniform Bose gas. We include the off-diagonal (anomalous)
pair correlations, and thus we have to introduce an off-diagonal distribution
function in addition to the normal (diagonal) distribution function. This
results in two coupled kinetic equations. If the off-diagonal distribution
function can be neglected as a higher-order contribution, we obtain the
semi-classical kinetic equation recently used by Zaremba, Griffin and Nikuni
(based on the simpler Popov approximation). We discuss the static local
equilibrium solution of our coupled HFB kinetic equations within the
semi-classical approximation. We also verify that a solution is the rigid
in-phase oscillation of the equilibrium condensate and non-condensate density
profiles, oscillating with the trap frequency.Comment: 25 page
Bose condensates in a harmonic trap near the critical temperature
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 condensate and low-lying quasiparticle excitations are calculated
self-consistently using the discrete variable representation, while the most
high-lying states are obtained with a local density approximation. Consistency
of the theory for temperatures through the Bose condensation point requires
that the thermodynamic chemical potential differ from the eigenvalue of the GP
equation; the appropriate modifications lead to results that are continuous as
a function of the particle interactions. The HFB equations are made gapless
either by invoking the Popov approximation or by renormalizing the particle
interactions. The latter approach effectively reduces the strength of the
effective scattering length, increases the number of condensate atoms at each
temperature, and raises the value of the transition temperature relative to the
Popov approximation. The renormalization effect increases approximately with
the log of the atom number, and is most pronounced at temperatures near the
transition. Comparisons with the results of quantum Monte Carlo calculations
and various local density approximations are presented, and experimental
consequences are discussed.Comment: 15 pages, 11 embedded figures, revte