Related papers: The Stochastic Gross-Pitaevskii Methodology
We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The discovered coherent structures…
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…
The dynamics of vortices in Bose-Einstein condensates of dilute cold atoms can be well formulated by Gross-Pitaevskii equation. To better understand the properties of vortices, a systematic method to solve the nonlinear differential…
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre…
The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use a scaling solution method comprising a time-dependent scaling function to analytically examine the dynamics of a falling Bose-Einstein…
We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an…
We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory we derive a zero-temperature modified Gross-Pitaevskii equation with beyond-mean-field corrections due to quantum…
We investigate the thermodynamic behaviour of a Bose gas interacting with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on…
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators…
We quantize the recent hydrodynamic analysis of Stringari for the low-energy collective modes of a trapped Bose gas at $T=0$. This is based on the time-dependent Gross-Pitaevskii equation, but omits the kinetic energy of the density…
We study the ground-state properties of dilute Bose gas confined to both isotropic and anisotropic traps to assess the accuracy of Gross-Pitaevskii (GP) theory. To go beyond GP approximation we use Huang-Yang theory of interatomic…
This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using…
I review the Bose-Einstein condensation phase transition of dilute gases of cold atoms, for particle theorists acquainted with methods of field theory at finite temperature. I then discuss how the dependence of the phase transition…
Following the idea of the density functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap, by using a local chemical potential - calculated with the Lieb-Liniger…
The weakly interacting trapped Bose gases have been customarily described using the mean-field approximation in the form of the Gross-Pitaevskii equation. The mean-field approximation, however, has certain limitations, in particular it can…
A mean-density description of spatially-inhomogeneous Bose-condensed gases based on Bogoliubov's method is introduced. The description assumes only a large mean atomic density and so remains valid when the mean field collapses due to phase…
Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with…
We derive a kinetic theory for a spin-1/2 Bose-condensed gas of two-level atoms at finite temperatures. The condensate dynamics is described by a generalized Gross-Pitaevskii equation for the two-component spinor order parameter, which…
The method of phenomenological damping developed by Pitaevskii for superfluidity near the $\lambda$ point is simulated numerically for the case of a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study several…
We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and…