4 research outputs found
Equivalence of Kinetic Theories of Bose-Einstein Condensation
We discuss the equivalence of two non-equilibrium kinetic theories that
describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a
harmonic trap. The second-order kinetic equations of Walser et al. [PRA 63,
013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum
Boltzmann equation in the low and high temperature limits, respectively. These
kinetic equations can thus describe the system in equilibrium (finite
temperature) as well as in non-equilibrium (real time). We have found this
theory to be equivalent to the non-equilibrium Green's function approach
originally proposed by Kadanoff and Baym and more recently applied to
inhomogeneous trapped systems by M. Imamovi\'c-Tomasovi\'c and A. Griffin
[arXiv:cond-mat/9911402].Comment: REVTeX3, 6 pages, 2 eps figures, published version, minor change
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
Collisionless dynamics of dilute Bose gases: Role of quantum and thermal fluctuations
We study the low-energy collective oscillations of a dilute Bose gas at
finite temperature in the collisionless regime. By using a time-dependent
mean-field scheme we derive for the dynamics of the condensate and
noncondensate components a set of coupled equations, which we solve
perturbatively to second order in the interaction coupling constant. This
approach is equivalent to the finite-temperature extension of the Beliaev
approximation and includes corrections to the Gross-Pitaevskii theory due both
to quantum and thermal fluctuations. For a homogeneous system we explicitly
calculate the temperature dependence of the velocity of propagation and damping
rate of zero sound. In the case of harmonically trapped systems in the
thermodynamic limit, we calculate, as a function of temperature, the frequency
shift of the low-energy compressional and surface modes.Comment: 26 pages, RevTex, 8 ps figure