Related papers: The Stochastic Gross-Pitaevskii Methodology
Momentum distributions and temporal power spectra of nonzero temperature Bose-Einstein condensates are calculated using a Gross-Pitaevskii model. The distributions are obtained for micro-canonical ensembles (conservative Gross-Pitaevskii…
We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the…
We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate…
We develop the number-conserving approach that has previously been used in a single component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an $n$-component…
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise.…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
A nonuniform condensate is usually described by the Gross-Pitaevskii (GP) equation, which is derived with the help of the c-number ansatz $\hat{ \Psi}(\mathbf{r},t)=\Psi (\mathbf{r},t)$. Proceeding from a more accurate operator ansatz…
A straight forward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally-excited states of a dilute boson gas. The process of evaporative cooling is then modelled by…
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…
We use the quantum kinetic theory to calculate the steady state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. The system is divided in a condensate and a non-condensate part. A quantum mechanical…
In experiments, Bose-Einstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is…
The study of the non-equilibrium dynamics in Bose-Einstein condensed gases has been dominated by the zero-temperature, mean field Gross-Pitaevskii formalism. Motivated by recent experiments on the reflection of condensates from silicon…
We obtain approximations for the time-independent Gross-Pitaevskii (GP) and complex GP equation in two and three spatial dimensions by generalizing the divergence-free WKB method. The results include an explicit expression of a uniformly…
We improve on the Popov theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. As a result, the theory becomes valid in arbitrary dimensions and is able to describe the low-temperature…
Stochastic field equations represent a powerful tool to describe the thermal state of a trapped Bose gas. Often, such approaches are confronted with the old problem of an ultraviolet catastrophe, which demands a cutoff at high energies. In…
We investigate dynamics in two-component Bose-Einstein condensates in the context of coupled Gross-Pitaevskii equations and derive results for the evolution of the total density fluctuations. Using these results, we show how, in many cases…
We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a {\em rotating} dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas…
We develop a practical theoretical formalism for studying the critical properties of a trapped Bose-Einstein condensate using the projected Gross-Pitaevskii equation. We show that this approach allows us investigate the behavior of the…
We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and…
In this paper, we develop a numerical procedure for investigating the dynamics of trapped Bose gases based on the ZGN theory. The dynamical equations used consist of a generalized Gross-Pitaevskii equation for the condensate order parameter…