Spectral analysis and time-dependent scattering theory on manifolds with asymptotically cylindrical ends

Autor:	Richard, S., de Aldecoa, R. Tiedra
Rok vydání:	2011
Předmět:	Mathematical Physics Mathematics - Differential Geometry Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.5018 Zobrazit plný text záznamu View this record from Arxiv