Beyond Bogoliubov dynamics
Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726.
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https://doi.org/10.48550/arXiv.1912.11004
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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.
Publishing Year
Date Published
2021-10-01
Journal Title
Pure and Applied Analysis
Publisher
Mathematical Sciences Publishers
Acknowledgement
We are grateful for the hospitality of Central China Normal University (CCNU),
where parts of this work were done, and thank Phan Th`anh Nam, Simone
Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research
Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding
from the European Union’s Horizon 2020 research and innovation programme under the Marie
Sk lodowska-Curie Grant Agreement No. 754411.
Volume
3
Issue
4
Page
677-726
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Cite this
Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 2021;3(4):677-726. doi:10.2140/paa.2021.3.677
Bossmann, L., Petrat, S. P., Pickl, P., & Soffer, A. (2021). Beyond Bogoliubov dynamics. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2021.3.677
Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.677.
L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021.
Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726.
Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:10.2140/paa.2021.3.677.
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arXiv 1912.11004