Abstract:
In this paper we study a two dimensional magnetic field Schrödinger 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].
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Received: 12 February 1997 / Accepted: 26 February 1997
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Mântoiu, M., Purice, R. Some Propagation Properties of the Iwatsuka Model . Comm Math Phys 188, 691–708 (1997). https://doi.org/10.1007/s002200050183
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DOI: https://doi.org/10.1007/s002200050183