相关论文: Commutative diagram of the Gross-Pitaevskii approx…
We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive non-linear Schr\"odinger functional whose quartic term is proportional to the scattering length of the…
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in…
The ground state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We present here the first proof of the asymptotic…
We consider Bose gases consisting of $N$ particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state energy…
We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number $N$ becomes large. In the dilute regime, when the interaction potentials have the length scale of order $O(N^{-1})$, we show…
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii…
We consider systems of $N$ bosons in $\mathbb{R}^3$, trapped by an external potential. The interaction is repulsive and has a scattering length of the order $N^{-1}$ (Gross-Pitaevskii regime). We determine the ground state energy and the…
We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is…
We consider a system of $N$ bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in $N$ (Gross-Pitaevskii regime). In this…
We study a dilute system of $N$ interacting bosons coupled to an impurity particle via a pair potential in the Gross--Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that…
For discrete and continuous Gross-Pitaevskii energy functionals with a random background potential, we study the Gross-Pitaevskii ground state. We characterize a regime of interaction coupling when the Gross-Pitaevskii ground state and the…
Using the linearized version of the time dependent Gross-Pitaevskii equation we calculate the dynamic response of a Bose-Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the…
We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitaevskii regime was recently solved by proving a link with the…
In the theoretical description of recent experiments with dilute Bose gases confined in external potentials the Gross-Pitaevskii equation plays an important role. Its status as an approximation for the quantum mechanical many-body ground…
We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number $N$ is large but $\bar\rho a^2$…
We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson's upper bound, which provides the correct leading order asymptotics for hard spheres. Afterwards, we discuss a rigorous version of…
The results of a modified Gross-Pitaevskii equation for a system of Bose hard spheres trapped in a spherical harmonic potential are analyzed to study the validity regime of the standard GP equation.
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 review probabilistic approaches to the Gross-Pitaevskii theory describing interacting dilute systems of particles. The main achievement are large deviations principles for the mean occupation measure of a large system of interacting…
We consider a gas of $N$ bosons in a box with volume one interacting through a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently small, we show that…