Asymptotic analysis of quantum scattering under mesoscopic scaling

Article type: Research Article

Authors: Benedetto, D.^; | Esposito, R.^; | Pulvirenti, M.

Affiliations: Dipartimento di Matematica Università di Roma ‘La Sapienza’, P.le A. Moro, 5, 00185 Roma, Italy | Centro Linceo Interdisciplinare “Beniamino Segre”, Via della Lungara 10, 00165 Roma, Italy | Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, Coppito, 67100 L'Aquila, Italy

Note: [] Corresponding author.

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.

Journal: Asymptotic Analysis, vol. 40, no. 2, pp. 163-187, 2004