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Beyond Bogoliubov Dynamics

Date: Thursday, January 30, 2020 16:00 - 18:00
Speaker: Sören Petrat (Jacobs University Bremen)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Robert Seiringer

In this talk 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.
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