Interacting bosons in a double-well potential : localization regime
Abstract
We study the ground state of a large bosonic system trapped in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of particles. In this context, one should expect an interaction-driven transition between a delocalized state (particles are independent and all live in both wells) and a localized state (particles are correlated, half of them live in each well). We start from the full many-body Schr{\"o}dinger Hamiltonian in a large-filling situation where the on-site interaction and kinetic energies are comparable. When tunneling is negligible against interaction energy, we prove a localization estimate showing that the particle number fluctuations in each well are strongly suppressed. The modes in which the particles condense are minimizers of nonlinear Schr{\"o}dinger-type functionals.
Cite
@article{arxiv.1612.05758,
title = {Interacting bosons in a double-well potential : localization regime},
author = {Nicolas Rougerie and Dominique Spehner},
journal= {arXiv preprint arXiv:1612.05758},
year = {2018}
}
Comments
Comments on what is meant by localization added. The conjecture on the localization/delocalization transition has been modified based on more precise heuristics