06-355 Y. Strauss, L.P. Horwitz, A. Volovick

Approximate resonance states in the semigroup decomposition of resonance evolution (585K, PDF) Dec 4, 06

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Abstract. The semigroup decomposition formalism makes use of the functional model for $C_{\cdot 0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state deines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a backgrouond term. We discuss the case of multiple resonances and give a bound on the size of the backgrouond term. As an example we treat a simple problem of scattering from a square barrier potential on a half-line.

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