In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of Nd-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N- 1) - 1Nd βv(Nβ·) for β∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN) -norm to arbitrary precision in powers of N- 1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Bose-Einstein condensation
- Many-body quantum dynamics
- Mean-field scaling
- Norm approximation