Schrödinger operator on some graphs : stabilization and dispersive effects

In this talk we analyse the spectrum of the dissipative Schrödinger operator on binary tree-shaped networks. As applications, we study the stability of the Schrödinger system using a Riesz basis as well as the transfer function associated to the system. Moreover, we study the dispersive effects associated to the Schrödinger operator with potential on star-shaped network and to the free Schrödinger operator on a tadpole graph.