Papers › Stability of the one electron atom Schrödinger model with magnetic field in two dimensions
Stability of the one electron atom Schrödinger model with magnetic field in two dimensions
Ayoub Arraji, Saad Benjelloun, Salma Lahbabi
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We study the stability of the one electron atom Schr\"odinger model with self-generated magnetic field in two dimensions. The magnetic energy is taken of the general form K∫_(ℝ²) |B|ᵖ and we study the stability of the model as a function of the power p and the coupling constant K. We show that for p>3/2, the model is always stable, and for p<3/2, the model is always unstable. In the critical case p=3/2, there is a critical stability constant K_c, that we characterize in terms of zero modes of the Dirac-Weyl operator. The value of K_c is approximated using analytic and numerical methods.
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