Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime.

Abstract: We consider a system of N bosons confined in a unit box with periodic boundary conditions. We assume that the particles interact through a repulsive two-body potential with scattering length of order 1/N, i.e. the Gross-Pitaevskii regime. We establish a precise bound for the ground state energy E(N) of the system. While the leading contribution, of order N, to the energy has been known since the pioneering works of Lieb-Seiringer-Yngvason in the early 2000s, and the second order (of order one) corrections were more recently first determined by Boccato-Brennecke-Cenatiempo-Schlein, our estimate also resolves the next term in the asymptotic expansion of E(N), which is of the order (log N)/N, confirming Wu’s predictions in 1959.

Based on a joint work with Alessandro Olgiati, Diane Saint Aubin and Benjamin Schlein.

mathematical physicsspectral theory

Audience: researchers in the topic

Munich-Copenhagen-Santiago Mathematical Physics seminar

Series comments: The MAS-MP seminar series has now changed name to MCS-MP.

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