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}
}
  • Lea Bossmann
  • Published 2019
  • Physics, Mathematics
  • arXiv: Mathematical Physics
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
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References

SHOWING 1-10 OF 57 REFERENCES
Derivation of the 1d Gross–Pitaevskii Equation from the 3d Quantum Many-Body Dynamics of Strongly Confined Bosons
  • 9
  • PDF
Bosons in Disc-Shaped Traps: From 3D to 2D
  • 26
  • PDF
The NLS Limit for Bosons in a Quantum Waveguide
  • 11
  • PDF
The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution
  • 27
  • PDF
On the Time Dependent Gross Pitaevskii- and Hartree Equation
  • 7
  • PDF
A note on 2D focusing many-boson systems
  • 22
  • PDF
Quantitative Derivation of the Gross-Pitaevskii Equation
  • 96
  • PDF
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