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arXiv · 2208.00199

Weak Edgeworth expansion for the mean-field interacting Bose gas

Lea Boßmann·Sören Petrat
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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 an Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in $1/\sqrt{N}$ . 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.

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Lea Boßmann, Sören Petrat. 2022-07-30. Weak Edgeworth expansion for the mean-field interacting Bose gas. https://doi.org/10.1007/s11005-023-01698-4

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