Dispersion on certain Cartesian products of graphs

Publication date: 23 August 2022

Abstract: In this short note we prove a sharp dispersive estimate $|mathrm{e}^{mathrm{i} tH} f|_infty < t^{-d/3}|f|_1$ for any Cartesian product $mathbb{Z}^dmathopsquare G_F$ of the integer lattice and a finite graph. This includes the infinite ladder, $k$-strips and infinite cylinders, which can be endowed with certain potentials.

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

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