BZ Seminar in Analysis: Serena Cenatiempo (GSSI L'Aquila)

Upper bounds on the ground state energy of dilute hard-core bosons

In the last decades, since the first experimental realizations of Bose-Einstein condensates, the study of large bosonic systems has been a very active field of research both in physics and in mathematics. In this talk we address a question strictly related to condensation, namely the characterization of macroscopic observables. More precisely, we consider dilute Bose gases and we focus on the second order asymptotic expansion for the ground state energy, which is believed to exhibit a universal behaviour, independent on the detail of the interaction.
We present a new upper bound for a dilute gas of hard core bosons in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity while keeping the density fixed. Our result resolves the ground state energy up to an error of the order of the sub-leading correction. We also discuss the Gross-Pitaevskii regime, in which N hard spheres with radius of order 1/N move on the unit torus; in this setting, we show an upper bound for the energy, capturing the correct second order correction.
Based on joint works with G. Basti, A. Giuliani, A. Olgiati, G. Pasqualetti, B. Schlein.

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