Semiclassical Resolvent Estimates for Matrix Schrödinger Operators and Applications

We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application, we prove a resonance-free domain in trapping situations. These results generalize the well-known results of [4] [N. Burq, Lower bounds for shape resonances widths of long range Schrödinger operators, Amer. J. Math. 124(4) (2002) 677–735] in the case of scalar Schrödinger operators. In addition, we give an estimate on the scattering amplitude for Schrödinger operators with compactly supported matrix-valued potentials. © World Scientific Publishing Company.