Asymptotic analysis of quantum scattering under mesoscopic scaling

Abstract

We consider a quantum particle scattered by an obstacle localized around the origin. We look at the time evolution in a large space‐time scale, O(ε⁻¹), assuming as initial datum a suitable WKB state with an amplitude varying on scale ε⁻¹. We study asymptotic behavior of the solution when ε vanishes. Our analysis is complementary to the one performed by Nier (Transport Theory Statist. Phys. 24(4–5) (1995), 591–629; Ann. Sci. École Norm. Sup. (4) 29 (1996), 149–183) who studied the same problem directly in terms of the Wigner formalism.