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Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics. (English) Zbl 0813.35073

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”.
Reviewer: B.Helffer (Paris)

MSC:

35P25 Scattering theory for PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
47F05 General theory of partial differential operators
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