Approximate resonance states in the semigroup decomposition of resonance evolution

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

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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).

Funding

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).

FundersFunder number
Center for Advanced Studies in Mathematics
Minerva Foundation
Israel Science Foundation1282/05, 188/02
Ben-Gurion University of the Negev

    Fingerprint

    Dive into the research topics of 'Approximate resonance states in the semigroup decomposition of resonance evolution'. Together they form a unique fingerprint.

    Cite this