Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields

Mouez Dimassi (1) , Masaki Kawamoto , Vesselin Petkov (1)

1 IMB - Institut de Mathématiques de Bordeaux

In the presence of the homogeneous electric field and the homogeneous perpendicular magnetic field, the classical trajectory of a quantum particle on ${\mathbb R}^2$ moves with drift velocity which is perpendiculars to the electric and magnetic fields. For such Hamiltonians the absence of the embedded eigenvalues of perturbed Hamiltonian has been conjectured. In this paper one proves this conjecture for the perturbations which have sufficiently small support in direction of drift velocity.

Domaines: Equations aux dérivées partielles [math.AP]

Mouez Dimassi, Masaki Kawamoto, Vesselin Petkov. Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields. 2020. ⟨hal-02508562⟩