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A Note on the Binding Energy for Bosons in the Mean-field Limit
Published 24 Jul 2023 in math-ph and math.MP | (2307.13115v2)
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.
- V. Bach. Ionization energies of bosonic Coulomb systems. Lett. Math. Phys., 21:139–149, 1991.
- R. Benguria and E. H. Lieb. Proof of the stability of highly negative ions in the absence of the Pauli principle. Phys. Rev. Lett., 50(22):1771–1774, 1983.
- Bogoliubov theory in the Gross–Pitaevskii limit. Acta Math., 222(2):219–335, 2019.
- N. N. Bogoliubov. On the theory of superfluidity. Izv. Akad. Nauk Ser. Fiz., 11:23–32, 1947.
- L. Boßmann. Low-energy spectrum and dynamics of the weakly interacting bose gas. J. Math. Phys., 2022.
- Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications. In A. Bassi, S. Goldstein, R. Tumulka, N. Zanghi (eds), Physics and the Nature of Reality, volume 215 of Fundamendal Theories of Physics. Springer, Cham, 2024.
- L. Boßmann and S. Petrat. Edgeworth expansion for the weakly interacting Bose gas. Lett. Math. Phys., 113(4):77, 2023.
- Beyond Bogoliubov dynamics. Pure Appl. Anal., 3(4):677–726, 2021.
- Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum Math. Sigma, 9:e28, 2021.
- Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Rev. Math. Phys., 35(4):2350006, 2022.
- P. Grech and R. Seiringer. The excitation spectrum for weakly interacting bosons in a trap. Commun. Math. Phys., 322(2):559–591, 2013.
- Derivation of Hartree’s theory for generic mean-field Bose systems. Adv. Math., 254:570–621, 2014.
- Bogoliubov spectrum of interacting Bose gases. Commun. Pure Appl. Math., 68(3):413–471, 2015.
- E. H. Lieb. Thomas–Fermi and related theories of atoms and molecules. Rev. Modern Phys., 53:603–641, 1981.
- The Mathematics of the Bose Gas and its Condensation. Birkhäuser, 2005.
- D. Mitrouskas. Derivation of mean field equations and their next-order corrections: Bosons and fermions. PhD thesis, 2017.
- P. T. Nam. Contributions to the rigorous study of the structure of atoms. PhD thesis, 2011.
- P. T. Nam. Binding energy of homogeneous Bose gases. Lett. Math. Phys., 108(1):141–159, 2018.
- R. Seiringer. The excitation spectrum for weakly interacting bosons. Commun. Math. Phys., 306(2):565–578, 2011.
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