Resonance free regions for systems of semiclassical Schrodinger operators and applications (Spectral and Scattering Theory and Related Topics)

Abstract

We consider an N × N system of semiclassical differential operators with N Schrödinger operators in the diagonal part and small interactions of order h^ν, where h is a semiclassical parameter and ν is a constant larger than one. We study the absence of resonance near a non-trapping energy for each Schrödinger operators. The width of resonances is estimated from below by Mh log(1/h) and the coefficient M can be taken propotional to ν - 1.