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

2023/10/25 by Félix Ali Mehmeti, Kaïs Ammari, Mehmeti, Felix Ali +3
Mathematics · #34B45 #34L25 #35B20 #35B40 #47A60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2310.16628

openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the free Schrödinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the L¹ to L^∞ 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.

Related

• Dispersive effects for the Schrödinger equation on a tadpole graph
• Dispersive effects and high frequency behaviour for the Schrödinger equation in star-shaped networks
• The Schrodinger Equation on a Star-Shaped Graph under General Coupling Conditions
• Dispersion for the Schrödinger Equation on Networks
• The Dispersion property for Schrödinger equations