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arXiv · 1912.11004

Beyond Bogoliubov Dynamics

Lea Boßmann·Sören Petrat·Peter Pickl·Avy Soffer
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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.

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Lea Boßmann, Sören Petrat, Peter Pickl, Avy Soffer. 2022-03-28. Beyond Bogoliubov Dynamics. https://doi.org/10.2140/paa.2021.3.677

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