AG Mathematische Physik, Wilhelm Kroschinsky (Bonn): The time-stability of Bose-Einstein,Condensates in the Gross-Pitaevskii,regime

Wilhelm Kroschinsky (Bonn)

The time-stability of Bose-Einstein Condensates in the Gross-Pitaevskii regime

Abstract:
We revisit the problem of time-stability of Bose-Einstein condensate (BEC) of an initially trapped
3D system of bosons in the Gross-Pitaevskii regime. We prove that the system still exhibits BEC
when the trap is switched off, and the effective dynamics is governed by the solution of the time-
dependent Gross-Pitaevskii equation. Our main strategy is to control renormalized excitation
number operators with respect to the Schrödinger dynamics 𝑡 ↦ → 𝑒−𝑖𝐻𝑁 𝑡 , rather than controlling
the number of excitations with respect to a suitable excitation dynamics 𝑡 ↦ → 𝑒−𝐵𝑡 𝑒−𝑖𝐻𝑁 𝑡 .