Bosons in a double well: two-mode approximation and fluctuations
arXiv:2101.08690 · doi:10.2140/apde.2023.16.1885
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.
References in corpus (13)
- On the Dynamics of Large Particle Systems in the Mean Field Limit
- The excitation spectrum for weakly interacting bosons in a trap
- The Excitation Spectrum for Weakly Interacting Bosons
- Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
- Bosonic quadratic Hamiltonians
- Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
- Mean-field quantum dynamics for a mixture of Bose-Einstein condensates
- Derivation of the Hartree equation for compound Bose gases in the mean field limit
- Multivariate Central Limit Theorem in Quantum Dynamics
- Central Limit Theorem for Bose-Einstein Condensates
- Ground state energy of mixture of Bose gases
- Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
- Propagation of Chaos and Effective Equations in Kinetic Theory: a Brief Survey