Jecko Th.
Semiclassical resolvent estimates for Schr\"odinger matrix
operators with eigenvalues crossing.
(109K, LaTeX 2e)
ABSTRACT. For semiclassical Schr\"odinger matrix operators, we investigate the
semiclassical Mourre theory to derive semiclassical bounds for the
boundary values of the resolvent. We concentrate on the case where
the eigenvalues of the symbol cross. Under the non-trapping condition
on the eigenvalues of the symbol and under a condition on its matricial
structure, we obtain the desired bounds for codimension one crossings.
For codimension two crossings, we show that a geometrical condition
at the crossing must hold to get the existence of a global escape
function, required by the usual semiclassical Mourre theory.