Related papers: Particle-Number-Conserving Bogoliubov Approximatio…
In this paper, we study Bose-Einstein condensation of Rydberg-dressed atoms considering finite range interactions. We use Hartree-Fock-Bogoliubov approximation based on Mean-Field approach. Moreover, within this approximation modified by…
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 study the time-evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. Under a physically motivated assumption on the energy of the initial data, we show that condensation is preserved by the many-body…
Atomic Bose-Einstein condensates (BECs) can be viewed as macroscopic objects where atoms form correlated atom clusters to all orders. Therefore, the presence of a BEC makes the direct use of the cluster-expansion approach --- lucrative e.g.…
We consider a Bose gas consisting of $N$ particles in $\mathbb{R}^3$, trapped by an external field and interacting through a two-body potential with scattering length of order $N^{-1}$. We prove that low energy states exhibit complete…
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…
A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates…
The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other.…
This paper investigates numerical methods for approximating the ground state of Bose--Einstein condensates (BECs) by introducing two relaxed formulations of the Gross--Pitaevskii energy functional. These formulations achieve first- and…
We study the ground state of a uniform Bose gas at zero temperature in the Hartree-Fock-Bogoliubov (HFB) approximation. We find a solution of the HFB equations which obeys the Hugenholtz-Pines theorem. This solution imposes a macroscopic…
To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation…
We show that the quantum many-body state of Bose-Einstein condensates (BEC) consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state (GCS). At zero temerature, the non-condensate density…
In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a…
We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled…
We demonstrate parametric resonance in Bose-Einstein condensates (BECs) with attractive two-body interaction in a harmonic trap under parametric excitation by periodic modulation of the s-wave scattering length. We obtain nonlinear…
We consider the Bogoliubov vacuum state in the number-conserving Bogoliubov theory proposed by Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We show that in the particle representation the vacuum can be written in a simple diagonal form.…
Two-component Bose-Einstein condensates are considered within a number conserving version of the Bogoliubov theory. We show that the Bogoliubov vacuum state can be obtained in the particle representation in a simple form. We predict…
We report on some recent results concerning the dynamics of Bose-Einstein condensates, obtained in a series of joint papers with L. Erdos and H.-T. Yau. Starting from many body quantum dynamics, we present a rigorous derivation of a cubic…
It is demonstrated that the well-known Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate (BEC) driven by the time-periodic harmonic or inverted-harmonic potential. A formally exact solution…
The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian…