- 03-14 Vidian ROUSSE
- Landau-Zener Transitions for Eigenvalue Avoided Crossings in the Adiabatic and Born-Oppenheimer Approximations
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Jan 14, 03
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Abstract. In the Born-Oppenheimer approximation context, we study the propagation of Gaussian wave packets through the simplest type of eigenvalue avoided crossings of an electronic Hamiltonian $\Cc^4$ in the nuclear position variable. It yields a two-parameter problem: the mass ratio $\eps^4$ between electrons and nuclei and the minimum gap $\delta$ between the two eigenvalues. We prove that, up to first order, the Landau-Zener formula correctly predicts the transition probability from a level to another when the wave packet propagates through the avoided crossing in the two different regimes: $\delta$ being either asymptotically smaller or greater than $\eps$ when both go to $0$.