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Pré-Publication, Document De Travail Année : 2018

Interacting bosons in a double-well potential : localization regime

Résumé

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.
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Dates et versions

hal-01417039 , version 1 (15-12-2016)
hal-01417039 , version 2 (23-05-2017)
hal-01417039 , version 3 (17-01-2018)
hal-01417039 , version 4 (12-03-2018)

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Nicolas Rougerie, Dominique Spehner. Interacting bosons in a double-well potential : localization regime. 2018. ⟨hal-01417039v3⟩
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