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Bosons in a double
well: two-mode approximation and fluctuations
Alessandro Olgiati, Nicolas Rougerie and Dominique Spehner |
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Vol. 16 (2023), No. 8, 1885–1954
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Abstract |
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We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well) are macroscopically occupied, and we are concerned with deriving the corresponding effective Bose–Hubbard Hamiltonian. We prove an energy expansion, including the two-mode Bose–Hubbard energy and two independent Bogoliubov corrections (one for each potential well), and a variance bound for the number of particles falling inside each potential well. The latter is a signature of a correlated ground state in that it violates the central limit theorem. |
Keywords
many-body quantum mechanics, Bose–Einstein condensation,
Bose–Hubbard model, Bogoliubov theory
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Mathematical Subject Classification
Primary: 35Q40, 81V73, 82B10
Secondary: 47A75, 49S05
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Milestones
Received: 31 May 2021
Revised: 28 January 2022
Accepted: 16 March 2022
Published: 16 October 2023
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Authors |
| Alessandro Olgiati | |
| Institut fur Mathematik Universitat Zurich Zurich Switzerland |
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| Nicolas Rougerie | |
| École Normale Supérieure de Lyon
& CNRS, UMPA (UMR 5669) Lyon France |
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| Dominique Spehner | |
| Departamento de Ingeniería
Matemática Universidad de Concepción Concepción Chile |
Université Grenoble Alpes &
CNRS Institut Fourier & LPMMC Grenoble France |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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