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arXiv · 2310.16628

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

Felix Ali Mehmeti·Kaïs Ammari·Serge Nicaise
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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.

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Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise. 2023-10-25. Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends. https://arxiv.org/abs/2310.16628

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