PhD Defense Birger Brietzke – University of Copenhagen

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PhD Defense Birger Brietzke

Title: On the Second Order Correction to the Ground State Energy of the Dilute Bose Gas

In this thesis we consider a gas of interacting, identical, spin-less bosons in a thermodynamic box. We are interested in the ground state energy, which for low densities (diluteness) is described by the Lee-Huang-Yang (LHY) formula - a series expansion in the density that has been derived in the late 1950's.

In the introduction we discuss an alternate derivation of the LHY formula based on Bogolubov's approximation step, which presupposes Bose-Einstein condensation.

The second part contains a detailed proof, which establishes the LHY formula as a lower bound in a \emph{weak coupling} and \emph{low density} regime. While our proof is guided by Bogolubov's predictions, it is based on a two-step localization procedure, which allows us to prove adequate 'local condensation'.

Supervisor: Prof. Jan Philip Solovej, Math, University of Copenhagen

Assessment committee:

Prof. Bergfinnur Durhuus (Chairman), MATH, University of Copenhagen

Prof. Robert Seiringer, Institute of Science and Technology Austria

Prof. Horia Cornean, Math, Aalborg University