## Seminar Analysis and Mathematical Physics: Alessandro Olgiati (University of Zurich)

**Bosons in a double well: two-mode approximation and fluctuations**

We study the ground state properties of a system of bosonic particles trapped by a double-well potential, in the limit of large inter-well separation and of high potential barrier. The N bosons also interact via a mean-field two-body potential, in the limit of large N.

The leading-order physics is governed by a Bose-Hubbard Hamiltonian coupling two low-energy modes, each supported in the bottom of one well. Fluctuations beyond these two modes are ruled by two independent Bogoliubov Hamiltonians, one for each well.

Our main result is that the variance of the number of particles in the low-energy modes is suppressed. This is a violation of the Central Limit Theorem which holds in the occurrence of Bose-Einstein condensation, and therefore it signals that particles develop correlations in the ground state. We achieve our result by proving a precise energy expansion in term of Bose-Hubbard and Bogoliubov energies.

Joint work with Nicolas Rougerie (ENS Lyon) and Dominique Spehner (Universidad de Concepción).

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