Beyond Bogoliubov Dynamics
Abstract
We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions.
Cite
@article{arxiv.1912.11004,
title = {Beyond Bogoliubov Dynamics},
author = {Lea Boßmann and Sören Petrat and Peter Pickl and Avy Soffer},
journal= {arXiv preprint arXiv:1912.11004},
year = {2022}
}
Comments
51 pages; v2: revised and extended version; v3: streamlined presentation; v4: this version appeared in Pure Appl. Analysis