dorsal/arxiv
View SchemaApproximate resonance states in the semigroup decomposition of resonance evolution
| Authors | Y. Strauss, L. P. Horwitz, A. Volovick |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612027 |
| URL | https://arxiv.org/abs/quant-ph/0612027 |
| DOI | 10.1063/1.2383069 |
Abstract
The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ 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 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.
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"abstract": "The semigroup decomposition formalism makes use of the functional model for\n$C_{.0}$ class contractive semigroups for the description of the time evolution\nof resonances. For a given scattering problem the formalism allows for the\nassociation of a definite Hilbert space state with a scattering resonance. This\nstate defines a decomposition of matrix elements of the evolution into a term\nevolving according to a semigroup law and a background term. We discuss the\ncase of multiple resonances and give a bound on the size of the background\nterm. As an example we treat a simple problem of scattering from a square\nbarrier potential on the half-line.",
"arxiv_id": "quant-ph/0612027",
"authors": [
"Y. Strauss",
"L. P. Horwitz",
"A. Volovick"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2383069",
"title": "Approximate resonance states in the semigroup decomposition of resonance evolution",
"url": "https://arxiv.org/abs/quant-ph/0612027"
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