01-428 Jecko Th.

Semiclassical resolvent estimates for Schr\"odinger matrix operators with eigenvalues crossing. (109K, LaTeX 2e) Nov 20, 01

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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.

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