Seminarium KMMF "Teoria Dwoistości"

Within the class of Dereziński pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known [De], we show that all entries of the N -body quantum scattering matrix have a well-defined meaning at any given non-threshold energy. As a function of the energy parameter the scattering matrix is weakly continuous. This result generalizes a similar one obtained previously by Yafaev for systems of particles interacting by short-range potentials [Ya1]. As for Yafaev’s paper we do not make any assumption on the decay of channel eigenstates. The main part of the proof consists in establishing a number of Kato-smoothness bounds needed for justifying a new formula for the scattering matrix. Similarly we construct and show strong continuity of channel wave matrices for all non-threshold energies. Away from a set of measure zero we show that the scattering and channel wave matrices constitute a well-defined ‘scattering theory’, in particular at such energies the scattering matrix is unitary and strongly continuous. To attend this ONLINE seminar you can meet us in room 2.23 or to use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09