Rigorous Derivation of the Gross-Pitaevskii Equation
Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau
TL;DR
This paper provides a rigorous mathematical proof that the Gross-Pitaevskii equation accurately describes the dynamics of Bose-Einstein condensates starting from the many-body Schrödinger equation with short-range interactions.
Contribution
It offers a rigorous derivation of the Gross-Pitaevskii equation from first principles, including the persistence of short-scale correlations in the condensate.
Findings
Confirmed the validity of the Gross-Pitaevskii equation in the dilute limit.
Demonstrated the persistence of short-scale correlation structures.
Provided a rigorous mathematical framework for the derivation.
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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