Analytic wave front set for solutions to Schrödinger equations

This paper is a continuation of [A. Martinez, S. Nakamura, V. Sordoni, Analytic smoothing effect for the Schrödinger equation with long-range perturbation, Comm. Pure Appl. Math. LIX (2006) 1330–1351], where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian H0 on Rn. In this paper, we consider short-range type perturbations H of the Laplacian on Rn, and we characterize the analytic wave front set of the solution to the Schrödinger equation: e−itHf, in terms of that of the free solution: e−itH0f, for t<0 in the forward non-trapping region. The same result holds for t>0 in the backward non-trapping region. This result is an analytic analogue of results by Hassel and Wunsch [A. Hassel, J. Wunsch, The Schrödinger propagator for scattering metrics, Ann. of Math. 162 (2005) 487–523] and Nakamura [S. Nakamura, Wave front set for solutions to Schrödinger equations, J. Funct. Anal. 256 (2009) 1299–1309].