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

Abstract

In the presence of the homogeneous electric field $\mathbf{E}$ and the homogeneous perpendicular magnetic field $\mathbf{B}$, the classical trajectory of a quantum particle on ${\mathbb{R}}^2$ moves with drift velocity $\alpha$ which is perpendicular 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 $V(x,y)$ which have sufficiently small support in direction of drift velocity.

Lemma 2.3 in the previous version is false and a counterexample is presented in Appendix A. In the improuved version we estabish Lemmas 2.2, 2.3 and 2.7 which are used to change the arguments

References in corpus (1)

• Semi-classical resolvent estimates for l $\infty$ potentials on Riemannian manifolds

Cited by in corpus (1)

• Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance