Semi-classical analysis of a Dirac equation without adiabatic decoupling (635K, Postscript) Mar 21, 03
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Abstract. We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a small coefficient which is a function of the semi-classical parameter. Therefore, the system presents an avoided crossing. There exists a critical scale which separates two situations. In one of them, adiabatic decoupling holds while for the other, 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 a Landau-Zener formula which takes into account the change of polarization of the measures after the crossing.

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