2016/12/17 by Nicolas Rougerie, Rougerie, Nicolas, Dominique Spehner +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum Gases (cond-mat.quant-gas) #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1612.05758
openalex publication_date 2016/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger 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 Schrödinger-type functionals.