Related papers: Quantum fluctuations and Gross-Pitaevskii theory
In the mean-field approximation, the number density \rho(r) for the ground state of a Bose-Einstein condensate trapped by an external potential V(r) satisfies a classical field equation called the Gross-Pitaevskii equation. We show that…
We study the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are: 1) to investigate dynamical regimes at the borderline between the classical and quantum behaviour of the…
Starting from first principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevskii equation, giving a bound on the rate of the convergence.…
We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian…
The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any…
Starting with a scalar field in a thermal bath and using the one loop quantum correction potential, we rewrite the Klein-Gordon equation in its thermodynamical representation and study the behavior of this scalar field due to temperature…
We extend the Projected Gross Pitaevskii equation formalism of Davis et al. [Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case of harmonic potentials. We outline a robust and accurate numerical scheme that can…
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…
We clarify that an ideal gas obeying infinite statistics cannot undergo condensation. Then we derive the dynamic equation for an identical particle system obeying infinite statistics under external potential and inter-particle interaction.…
We develop formalism based on the projected Gross Pitaevskii equation to simulate the finite temperature collective mode experiments of Jin et al. [PRL 78, 764 (1997)]. We examine the $m=0$ and $m=2$ quadrupolar modes on the temperature…
We study the effects of quantum and thermal fluctuations on Bose-Bose mixtures at finite temperature employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The theory governs selfconsistently the motion of the condensates, the…
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…
Quantum fluctuations in time-dependent, harmonically-trapped Bose-Einstein condensates are studied within Bogoliubov theory. An eigenmode expansion of the linear field operators permits the diagonalization of the Bogoliubov-de Gennes…
We investigate quantum gravity corrections due to the generalized uncertainty principle on three-dimensional weakly interacting Bose gases at both zero and finite temperatures using the time-dependent Hatree-Fock-Bogoliubov theory. We…
The correlation function of the quantum fluctuations due to collective excitations is calculated and used to investigate the phase diffusion of a Bose-Einstein condensate close to zero temperature. It is shown that the phase diffusion time…
Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a…
We consider a homogeneous Bose gas in the Gross-Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose-Einstein condensation in the ideal gas. Our main result is an upper bound for the grand canonical free…
Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The…
We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D…
For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of…