We consider the Schrödinger equation associated to long range perturbations of the flat Euclidean metric (in particular, potentials growing subquadratically at infinity are allowed). We construct a modified quantum free evolution G(s) acting on Sjöstrand’s spaces, and we characterize the analytic wave front set of the solution e?itH u_0 of the Schrödinger equation, in terms of the semiclassical exponential decay of G(?th^{?1})Tu_0, where T stands for the Bargmann-transform. The result is valid for t < 0 near the forward non-trapping points, and for t > 0 near the backward non-trapping points.

Analytic Singularities for Long Range Schr"odinger Equations

MARTINEZ, ANDRE' GEORGES;SORDONI, VANIA;
2008

Abstract

We consider the Schrödinger equation associated to long range perturbations of the flat Euclidean metric (in particular, potentials growing subquadratically at infinity are allowed). We construct a modified quantum free evolution G(s) acting on Sjöstrand’s spaces, and we characterize the analytic wave front set of the solution e?itH u_0 of the Schrödinger equation, in terms of the semiclassical exponential decay of G(?th^{?1})Tu_0, where T stands for the Bargmann-transform. The result is valid for t < 0 near the forward non-trapping points, and for t > 0 near the backward non-trapping points.
A. Martinez; V. Sordoni; S. Nakamura
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/61904
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