Yves Colin de Verdiere
Bohr-Sommerfeld phases for
avoided crossings
(407K, Postscript)

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.