BEYOND BOGOLIUBOV DYNAMICS
Boßmann L, Petrat S, Pickl P, Soffer A (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 3
Pages Range: 677-726
Journal Issue: 4
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 correlation functions of a quasifree 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 correlation functions.
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Germany (DE)How to cite
APA:
Boßmann, L., Petrat, S., Pickl, P., & Soffer, A. (2021). BEYOND BOGOLIUBOV DYNAMICS. Pure and Applied Analysis, 3(4), 677-726. https://doi.org/10.2140/paa.2021.3.677
MLA:
Boßmann, Lea, et al. "BEYOND BOGOLIUBOV DYNAMICS." Pure and Applied Analysis 3.4 (2021): 677-726.
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