Some Propagation Properties of the Iwatsuka Model

In this paper we study a two dimensional magnetic field Schr?dinger Hamiltonian introduced in 7]. This model has some interesting propagation properties, as conjectured in 2] and at the same time is a special case of the class of analytically decomposable Hamiltonians 5]. Our aim is to start from a conjugate operator, intimately related to the band structure of the Hamiltonian and to prove existence of an asymptotic velocity in one spatial direction and a theorem giving minimal and maximal velocity bounds for the propagation associated to the Hamiltonian. A simple example of this model, with a very simple conjugate operator, has been given in 9]. At the same time, by using the Virial Theorem, we obtain a generalisation of the hypothesis in 7]. Received: 12 February 1997 / Accepted: 26 February 1997