Related papers: Another proof of BEC in the GP-limit
We discuss the mean-field approximation for a trapped weakly-interacting Bose-Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross-Pitaevskii action of the condensate. The mechanics of the BEC…
We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC). The main interest in such BEC comes from its important nature as macroscopic quantum…
In this work, we investigate the stability aspects of quintic Gross-Pitaevskii (GP) equation with the presence and absence of external trapping potential for a Bose Gas (BG) in both the Tonks-Girardeau (TG) and the super Tonks-Girardeau…
We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross-Pitaevskii (GP) limit, where the scattering length $a$ is so small that the interaction energy is of the same order of magnitude as…
By numerical and variational solution of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the…
We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution 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…
Bose-Einstein condensate of rarified atomic gases is considered as the state formed by exchange of virtual photons, resonant to the lowest levels of atoms; such representation corresponds to the Einstein opinion about an inter-influence of…
We revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is…
Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity) we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a…
We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with…
We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang {\it et al.}…
Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to…
We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation…
The low-energy-level macroscopic wave functions of the Bose-Einstein condensate(BEC) trapped in a symmetric double-well and a periodic potential are obtained by solving the Gross-Pitaevskii equation numerically. The ground state tunnel…
Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic…
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 consider N bosons on the unit torus $\Lambda = [0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V (N(x -y))$. We prove that the thermal equilibrium at low temperatures exhibits the Bose-Einstein…
We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. These nonlinear localized solutions play a central role in the…
By taking the hydrodynamic limit we derive, at $T=0$, an explicit solution of the linearized time dependent Gross-Pitaevskii equation for the order parameter of a Bose gas confined in a harmonic trap and interacting with repulsive forces.…