Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends

Felix Ali Mehmeti; Kaïs Ammari; Serge Nicaise

Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends

Analysis of PDEs 2024-09-13 v2

Authors: Felix Ali Mehmeti , Kaïs Ammari , Serge Nicaise

Abstract

We study the free Schr\"odinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$ time decay rate at least $t^{-1/2}$ . These conditions allow certain metric graphs with circles and/or with commensurable lengths of the bounded edges. Further we study the dynamics of the probability flow between the bounded sub-graph and the unbounded ends.

Keywords

schrödinger equation metric graphs infinite ends dispersive estimates l1-l∞ decay probability flow

Cite

@article{arxiv.2310.16628,
  title  = {Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends},
  author = {Felix Ali Mehmeti and Kaïs Ammari and Serge Nicaise},
  journal= {arXiv preprint arXiv:2310.16628},
  year   = {2024}
}

Comments

34 pages, 6 figures, 29 references; major revisions with respect to the first version of october 2023

Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends

Abstract

Keywords

Cite

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