相关论文: Note on the Zero-Energy-Limit Solution for the Mod…
The ground state of the energy super-critical Gross--Pitaevskii equation with a harmonic potential converges in the energy space to the singular solution in the limit of large amplitudes. The ground state can be represented by a solution…
We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We describe the asymptotic dynamics of solutions to the corresponding…
We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the solution; in particular, conditions for optimal decay in…
We review the stochastic Gross-Pitaevskii approach for non-equilibrium finite temperature Bose gases, focussing on the formulation of Stoof; this method provides a unified description of condensed and thermal atoms, and can thus describe…
We consider a system of $N$ bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normalized thickness of the box $d\ll1$. We assume particles to…
In this study, after we have briefly introduced the standard Gross-Pitaevskii equation, we have suggested fractional Gross-Pitaevskii equations to investigate the time-dependent ground state dynamics of the Bose-Einstein condensation of…
We consider a homogeneous Bose gas in the Gross--Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose--Einstein condensation. Recently, an upper bound for the grand canonical free energy was proved in…
We derive the time-dependent dipolar Gross-Pitaevskii (GP) equation from the N-body Schr{\"o}dinger equation. More precisely we show a norm approximation for the solution of the many body equation as well as the convergence of its one-body…
We consider many-body effects on particle scattering in one, two and three dimensional Bose gases. We show that at zero temperature these effects can be modelled by the simpler two-body T-matrix evaluated off the energy shell. This is…
We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr\"odinger equation at the leading order in the number of particles. The…
We develop an approximate formalism suitable for performing simulations of the thermal dynamics of interacting Bose gases. The method is based on the observation that when the lowest energy modes of the Bose field operator are highly…
We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch…
In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current…
The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale…
We study the finite temperature dynamical structure factor $S(k,\omega)$ of a 1D Bose gas using numerical simulations of the Gross--Pitaevskii equation appropriate to a weakly interacting system. The lineshape of the phonon peaks in…
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…
We have achieved the first full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only…
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the Gross-Pitaevskii…
The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem…
It has been proven theoretically for bosons with two-body repulsive interaction potentials in the dilute limit that the Gross-Pitaevskii equation provides the exact energy and density per particle as does the basic many-particle…