Sojourn Times and Asymptotic Properties of the Scattering Matrix

Abstract

and their inverses exist and are, therefore, unitary operators from H to H intertwing U and ^LZ0. the scattering operator is S=W (W~), and it intertwines ^L£0 with itself. Now in the cases of interest for scattering theory HQ has a uniform continuous spectrum. This means there exists a Hilbert space K and an isomorphism of Hilbert spaces p:H-+L(R,K) such that p^lX^t) p~ is the operator by for (7EE.R. Since S commutes with ^o? pSp~* commutes with multiplication by e for all t, and must then necessarily be of the form by *S(0) where S(fi^):IC—>K is for each ff^R a unitary operator. The subject of this talk will be the asymptotic behavior of 5((T) for large values of (T. Our purpose will be to examine this asymptotic behavior in special cases and attempt to discern some general pattern.

Locations

• Publications of the Research Institute for Mathematical Sciences - View - PDF