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Séminaire Physique mathématique ICJ

# Derivation of nonlinear Gibbs measures from many-body quantum mechanics

## by Mr. Nicolas Rougerie (LPMMC, Grenoble)

vendredi 15 janvier 2016 de au (Europe/Paris)
at UCBL - Bât. braconnier ( Fokko du Cloux )
21 av. Claude Bernard 69100 Villeurbanne
 Description A great deal of progress has been made in recent years on the rigorous derivation of effective Non-Linear Schrödinger equations starting from N-body Schrödinger Hamiltonians. In particular, Bose-Einstein condensation of zero-temperature ground states of large bosonic systems has been derived for various models and asymptotic regimes. In this talk we shall discuss a similar limit for positive temperature equilibrium states of the many-body Schrödinger Hamiltonian. We start from grand-canonical Gibbs states and obtain non-linear Gibbs measures built on the NLS functional in the limit. Our method covers the case of 1D particles with repulsive contact interactions, and higher dimensional particles with a reguralized interaction. Joint work with Mathieu Lewin and Phan Thành Nam.