The Rigorous Derivation of the 2 D Cubic Focusing Nls from Quantum Many-body Evolution

@inproceedings{Chen2015TheRD,
  title={The Rigorous Derivation of the 2 D Cubic Focusing Nls from Quantum Many-body Evolution},
  author={Xuwen Chen and J. Holmer},
  year={2015}
}
We consider a 2D time-dependent quantum system of N -bosons with harmonic external confining and attractive interparticle interaction in the Gross-Pitaevskii scaling. We derive stability of matter type estimates showing that the k-th power of the energy controls the H Sobolev norm of the solution over k-particles. This estimate is new and more diffi cult for attractive interactions than repulsive interactions. For the proof, we use a version of the finite-dimensional quantum di Finetti theorem… CONTINUE READING

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