A note on the validity of Bogoliubov correction to meanfield dynamics
Abstract
We study the norm approximation to the Schrödinger dynamics of $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3\beta1}w(N^{\beta}(xy))$. Assuming that in the initial state the particles outside of the condensate form a quasifree state with finite kinetic energy, we show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all $0\le \beta<1/2$. The range of $\beta$ is expected to be optimal for this large class of initial states.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.05240
 Bibcode:
 2016arXiv160405240T
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs
 EPrint:
 Final version, to appear in Journal de Math\'ematiques Pures et Appliqu\'ees