Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics (Q1340846)

The main goal of this article is to compare two long-range perturbations of constant coefficients operators on \(\mathbb{R}^ n\) such that their difference is short range. Typical examples are semi-classical Schrödinger Hamiltonians such that the difference of the corresponding potentials is decreasing sufficiently rapidly at \(\infty\). In this context the average time-delay depending on the energy \(\lambda\) and on the semiclassical parameter \(h\) is well defined and the author studies its asymptotic behavior in the high-energy ``régime'' and in the semi- classical ``régime''.