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arXiv:2307.13115 · Journal of Statistical Physics

A Note on the Binding Energy for Bosons in the Mean-Field Limit

Lea Boßmann, Nikolai Leopold, David Mitrouskas, Sören Petrat

Published Apr 6, 2024• 0 citations
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Abstract

Abstract We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.

DOI
10.1007/s10955-024-03260-5

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Abstract We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.
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Abstract For a translation invariant system of N bosons in the Gross–Pitaevskii regime, we establish a precise bound for the ground state energy ENE_NEN​ E N . While the leading, order N , contribution to ENE_NEN​ E N has been known since (Lieb et al. in Phys Rev A 61:043602, 2000; Lieb and Yngvason in Phys Rev Lett 80:2504–2507, 1998) and the second order corrections (of order one) have been first determined in Boccato et al. (Acta Math 222(2):219–335, 2019), our estimate also resolves the next term in the asymptotic expansion of ENE_NEN​ E N , which is of the order (log⁡N)/N(\log N) / N(logN)/N ( log N ) / N .
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