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.
BOSONS IN A DOUBLE WELL: TWO-MODE APPROXIMATION AND FLUCTUATIONS
Olgiati A.;
2023-01-01
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 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.File | Dimensione | Formato | |
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