Resolvent estimates and resonance free domains for Schrödinger operators with matrix-valued potentials

Abstract: We establish semiclassical resolvent estimates for Schr\"odinger operators with long-range matrix-valued potentials. As an application we prove resonance free domains both in trapping and non-trapping situations. Our results generalize the well-known results of \cite{Burq1, Martinez1} in the case of scalar Schr\"odinger operators.