Abstract.
We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a coefficient ɛα where ɛ is the semi-classical parameter and α > 0. Therefore, the system presents an avoided crossing. The scale α = 1/2 is critical: adiabatic decoupling holds for α∈ (0,1/2) while for α ≥ 1/2, there is energy transfer at leading order between the two modes. We describe this transfer in terms of two-scale Wigner measures by means of Landau-Zener formula which takes into account the change of polarization of the measures after the crossing.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kammerer, C. Semi-Classical Analysis of a Dirac Equation Without Adiabatic Decoupling. Monatsh. Math. 142, 281–313 (2004). https://doi.org/10.1007/s00605-003-0145-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-003-0145-z