Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends
Abstract
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud-Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.
Keywords
Cite
@article{arxiv.1108.5018,
title = {Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends},
author = {S. Richard and R. Tiedra de Aldecoa},
journal= {arXiv preprint arXiv:1108.5018},
year = {2011}
}
Comments
30 pages