Frequency-dependent time decay of Schr\"odinger flows

@article{Fanelli2015FrequencydependentTD,
  title={Frequency-dependent time decay of Schr\"odinger flows},
  author={L. Fanelli and Veronica Felli and Marco Antonio Fontelos and Amedeo Primo},
  journal={arXiv: Analysis of PDEs},
  year={2015}
}
  • L. Fanelli, Veronica Felli, +1 author Amedeo Primo
  • Published 2015
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
  • We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schr\"odinger hamiltonian $H$ generically produces a lack of the classical time-decay for the associated Schr\"odinger flow $e^{-itH}$. This is in contrast with the fact that dispersive estimates (Strichartz) still hold, in general, also in this case. We also observe an improvement of the decay for higher positive modes, showing that the time decay of the solution is due to the first… CONTINUE READING

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