Approximate resonance states in the semigroup decomposition of resonance evolution

Y. Strauss, L. P. Horwitz, A. Volovick

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Abstract

The semigroup decomposition formalism makes use of the functional model for C0 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 defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.

Original languageEnglish
Article number123505
JournalJournal of Mathematical Physics
Volume47
Issue number12
DOIs
StatePublished - 2006

Bibliographical note

Funding Information:
The work of Y.S. was partially supported by ISF under Grants No. 1282/05 and No. 188/02, and by the Center for Advanced Studies in Mathematics at Ben-Gurion University and the Edmond Landau Center for research in Mathematical Analysis and related areas, sponsored by the Minerva Foundation (Germany).

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