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Nicolas Rougerie

Localized Regime for Mean-Field Bosons in a Double-Well Potential

Abstract:We study the many-body Schrödinger Hamiltonian for interacting bosons in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of particles. We focus on an interaction-driven transition in the ground state, 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). 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.

joint work with Dominique Spehner