Semi-Classical Analysis of a Dirac Equation Without Adiabatic Decoupling |
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Authors: | Clotilde Fermanian Kammerer |
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Institution: | (1) Université de Cergy-Pontoise, France |
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Abstract: | We study adiabatic decoupling for Dirac equation with some scaling which yields that the mass appears with a coefficient ![epsiv](/content/1nm6gjdr4bx07flk/xxlarge603.gif) where is the semi-classical parameter and > 0. Therefore, the system presents an avoided crossing. The scale = 1/2 is critical: adiabatic decoupling holds for ![agr](/content/1nm6gjdr4bx07flk/xxlarge945.gif) (0,1/2) while for 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. |
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Keywords: | 2000 Mathematics Subject Classification: 35Q40 35B 35L |
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