Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons
Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons
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 …