Dispersive effects for the Schrödinger equation on finite metric graphs with infinite ends

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 boun...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Felix Ali Mehmeti, Ammari, Kaïs, Nicaise, Serge
Format: Article
Language:English
Subjects:
Decay rate
Graphs
Schrodinger equation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422