Weak Edgeworth expansion for the mean-field Bose gas
Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77.
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Abstract
We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion.
Publishing Year
Date Published
2023-07-03
Journal Title
Letters in Mathematical Physics
Publisher
Springer Nature
Acknowledgement
It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee for many constructive comments. L.B. gratefully acknowledges funding from the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical Research Institute Oberwolfach, where part of this work was done, for their hospitality.
Open Access funding enabled and organized by Projekt DEAL.
Volume
113
Issue
4
Article Number
77
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Cite this
Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 2023;113(4). doi:10.1007/s11005-023-01698-4
Bossmann, L., & Petrat, S. P. (2023). Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-023-01698-4
Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s11005-023-01698-4.
L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field Bose gas,” Letters in Mathematical Physics, vol. 113, no. 4. Springer Nature, 2023.
Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77.
Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics, vol. 113, no. 4, 77, Springer Nature, 2023, doi:10.1007/s11005-023-01698-4.
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