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Rigorous Derivation of the Gross-Pitaevskii Equation

Laszlo Erdos·Benjamin Schlein·Horng-Tzer Yau
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Abstract

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.

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Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau. 2006-12-10. Rigorous Derivation of the Gross-Pitaevskii Equation. https://doi.org/10.1103/physrevlett.98.040404

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