We study sufficient conditions for the absence of positive eigenvalues of
    magnetic Schr\”odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main
    result we prove the absence of eigenvalues above certain threshold energy which
    depends explicitly on the magnetic and electric field. A comparison with the
    examples of Miller–Simon shows that our result is sharp as far as the decay of
    the magnetic field is concerned. As applications, we describe several
    consequences of the main result for two-dimensional Pauli and Dirac operators,
    and two and three dimensional Aharonov–Bohm operators.

    Source link


    Leave A Reply