• DOI:10.2140/paa.2021.3.677
• Corpus ID: 209444626

Beyond Bogoliubov dynamics

@article{Bomann2019BeyondBD,
  title={Beyond Bogoliubov dynamics},
  author={Lea Bo{\ss}mann and Soren Petrat and Peter Pickl and Avy Soffer},
  journal={Pure and Applied Analysis},
  year={2019}
}

• Lea Boßmann, S. Petrat, +1 author A. Soffer
• Published 23 December 2019
• Mathematics, Physics
• Pure and Applied Analysis

We consider a quantum system of N interacting bosons in the mean field scaling regime. We construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The corrections are such that they can be explicitly computed in an N-independent way from 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 mean field, as well as the reduced densities of the N-body system to arbitrary precision, 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 describing the two-point functions of the Bogoliubov time evolution, which are equations for a two-particle system.