Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons

@article{Bossmann2019DerivationOT,
title={Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons},
author={Lea Bossmann},
journal={arXiv: Mathematical Physics},
year={2019}
}

We study the dynamics of a system of $N$ interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to a region of order $\varepsilon$. The interaction is non-negative and scaled in such a way that its scattering length is of order $(N/\varepsilon)^{-1}$, while its range is proportional to $(N/\varepsilon)^{-\beta}$ with scaling parameter $\beta\in(0,1]$. The choice $\beta=1$ corresponds to the physically relevant Gross… Expand