Bosons in a double well: two-mode approximation and fluctuations
Mathematical Physics
2023-10-25 v3 math.MP
Abstract
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.
Cite
@article{arxiv.2101.08690,
title = {Bosons in a double well: two-mode approximation and fluctuations},
author = {Alessandro Olgiati and Nicolas Rougerie and Dominique Spehner},
journal= {arXiv preprint arXiv:2101.08690},
year = {2023}
}