A Rigorous Derivation of theGross - Pitaevskii Energy Fun tionalfor a Two - dimensional Bose GasElliott

A Rigorous Derivation of theGross - Pitaevskii Energy Fun tionalfor a Two - dimensional Bose

Institute for Mathematical Physics Bosons in a Trap: a Rigorous Derivation of the Gross{pitaevskii Energy Functional Bosons in a Trap: a Rigorous Derivation of the Gross-pitaevskii Energy Functional

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 rst proof of the asymptotic exactness of this approximation for the ground state energy and particle density of a dilute Bose gas with a positive interaction.

Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional

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 exactness of this approximation for the ground state energy and particle density of a dilute Bose gas with a positive interaction.

A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-dimensional Bose Gas

We consider the ground state properties of an inhomogeneous twodimensional 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 ρ̄a2 is small, where ρ̄ is the average particle density and a the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gr...

Rigorous derivation of the Gross-Pitaevskii equation.

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 Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.