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Article Dans Une Revue Analysis and partial differential equations Année : 2023

Bosons in a double well: two-mode approximation and fluctuations

Résumé

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 (i) an energy expansion, including the two-modes Bose-Hubbard energy and two independent Bogoliubov corrections (one for each potential well), (ii) 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.
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Dates et versions

hal-03117990 , version 1 (21-01-2021)
hal-03117990 , version 2 (23-05-2021)
hal-03117990 , version 3 (02-02-2022)

Identifiants

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Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner. Bosons in a double well: two-mode approximation and fluctuations. Analysis and partial differential equations, 2023, 16 (8), pp.1885-1954. ⟨10.2140/apde.2023.16.1885⟩. ⟨hal-03117990v3⟩
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