Related papers: Deriving the Gross-Pitaevskii equation
We report on some recent results regarding the dynamical behavior of a trapped Bose-Einstein condensate, in the limit of a large number of particles. These results were obtained in \cite{ESY}, a joint work with L. Erd\H os and H.-T. Yau.
We use the finite-temperature extended Gross-Pitaevskii equation (TeGPE) to study a condensate of dipolar NaCs molecules under the conditions of the very recent, breakthrough experiment [Bigagli et.al., Nature 631, 289 (2024)]. We report…
We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which contains initially many vortices at arbitrary locations. We present first the analytical solution of the dynamics in a homogeneous medium…
We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasi-periodic boundary conditions to investigate the behaviour…
We investigate the dynamic behavior of a Bose-condensed gas of alkali atoms interacting with repulsive forces and confined in a magnetic trap at zero temperature. Using the Thomas-Fermi approximation, we rewrite the Gross-Pitaevskii…
A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the…
We develop a general formalism applying to Newtonian self-gravitating Bose-Einstein condensates. This formalism may find application in the context of dark matter halos. We introduce a generalized Gross-Pitaevskii equation including a…
We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from \cite{BBCS,BBCS4}. While our main strategy is similar to the one developed in…
Non-relativistic interacting bosons at zero temperature, in two and three dimensions, are expected to exhibit a fascinating critical phase, famously known as condensate phase. Even though a proof of Bose-Einstein condensation in the…
Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the…
The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case…
We report a numerical study of turbulence and Bose-Einstein condensation within the two-dimmensional Gross-Pitaevski model with repulsive interaction. In presence of weak forcing localized around some wave number in the Fourier space, we…
In this work we investigate the unique properties of ultracold Bose gases in one and two dimensions. In two dimensions, we present simulations of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the projected…
The problem of wave breaking during its propagation in the Bose-Einstein condensate to a stationary medium is considered for the case when the initial profile at the breaking instant can be approximated by a power function of the form…
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…
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 analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a…
We derive a general and exact equation of motion for a quantised vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in…
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study…
We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy…