04-288 Yves Colin de Verdiere
Bohr-Sommerfeld phases for avoided crossings (407K, Postscript) Sep 16, 04
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Abstract. The Landau-Zener formula gives the local scattering matrix for systems of semi-classical pseudo-differential equations on the real line near an avoided crossing. In the present paper, we describe the global scattering matrix in the case of several avoided crossings. The interferences pattern is taken into account via ad'hoc Bohr-Sommerfeld phases associated to the cycles of the dispersion relation. In particular, we get results concerning the quantum adiabatic limit in the case of avoided crossings.

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